Yang-Hui He - Academia.edu (original) (raw)
Papers by Yang-Hui He
Physical Review D, 2003
We obtain explicit formulas for the Neumann coefficients and associated quantities that appear in... more We obtain explicit formulas for the Neumann coefficients and associated quantities that appear in the three-string vertex for type IIB string theory in a plane-wave background, for any value of the mass parameter mu. The derivation involves constructing the inverse of a certain infinite-dimensional matrix, in terms of which the Neumann coefficients previously had been written only implicitly. We derive asymptotic expansions for large mu and find unexpectedly simple results, which are valid to all orders in 1/mu. Using BMN duality, these give predictions for certain gauge theory quantities to all orders in the modified 't Hooft coupling lambda'. A specific example is presented.
Physical Review D, 2004
We investigate the general features of renormalization group flows near superconformal fixed poin... more We investigate the general features of renormalization group flows near superconformal fixed points of four dimensional N=1 supersymmetric gauge theories with gravity duals. The gauge theories we study arise as the world-volume theory on a set of D-branes at a Calabi-Yau singularity where a del Pezzo surface shrinks to zero size. Based mainly on field theory analysis, we find evidence that such flows are often chaotic and contain exotic features such as duality walls. For a gauge theory where the del Pezzo is the Hirzebruch zero surface, the dependence of the duality wall height on the couplings at some point in the cascade has a self-similar fractal structure. For a gauge theory dual to CP^2 blown up at a point, we find periodic and quasi-periodic behavior for the gauge theory couplings that does not violate the a-conjecture. Finally, we construct supergravity duals for these del Pezzos that match our field theory beta functions.
Fortschritte Der Physik-progress of Physics, 2006
Within the context of the E8 × E8 heterotic superstring compactified on a smooth Calabi-Yau three... more Within the context of the E8 × E8 heterotic superstring compactified on a smooth Calabi-Yau threefold with an SU(4) gauge instanton, we show the existence of simple, realistic N = 1 supersymmetric vacua that are compatible with low energy particle physics. The observable sector of these vacua has gauge group SU(3)C × SU(2)L × U(1)Y × U(1)B-L, three families of quarks and leptons, each with an additional right-handed neutrino, two Higgs-Higgs conjugate pairs, a small number of uncharged moduli and no exotic matter.
Physics Letters B, 2004
Explicit methods are presented for computing the cohomology of stable, holomorphic vector bundles... more Explicit methods are presented for computing the cohomology of stable, holomorphic vector bundles on elliptically fibered Calabi-Yau threefolds. The complete particle spectrum of the low-energy, four-dimensional theory is specified by the dimensions of specific cohomology groups. The spectrum is shown to depend on the choice of vector bundle moduli, jumping up from a generic minimal result to attain many higher values on subspaces of co-dimension one or higher in the moduli space. An explicit example is presented within the context of a heterotic vacuum corresponding to an SU (5) GUT in four-dimensions. *
Journal of High Energy Physics, 2006
We show the existence of realistic vacua in string theory whose observable sector has exactly the... more We show the existence of realistic vacua in string theory whose observable sector has exactly the matter content of the MSSM. This is achieved by compactifying the E_8 x E_8 heterotic superstring on a smooth Calabi-Yau threefold with an SU(4) gauge instanton and a Z_3 x Z_3 Wilson line. Specifically, the observable sector is N=1 supersymmetric with gauge group SU(3)_C x SU(2)_L x U(1)_Y x U(1)_{B-L}, three families of quarks and leptons, each family with a right-handed neutrino, and one Higgs-Higgs conjugate pair. Importantly, there are no extra vector-like pairs and no exotic matter in the zero mode spectrum. There are, in addition, 6 geometric moduli and 13 gauge instanton moduli in the observable sector. The holomorphic SU(4) vector bundle of the observable sector is slope-stable.
Journal of High Energy Physics, 2006
In this paper, we present a formalism for computing the non-vanishing Higgs mu-terms in a heterot... more In this paper, we present a formalism for computing the non-vanishing Higgs mu-terms in a heterotic standard model. This is accomplished by calculating the cubic product of the cohomology groups associated with the vector bundle moduli (phi), Higgs (H) and Higgs conjugate (Hbar) superfields. This leads to terms proportional to phi H Hbar in the low energy superpotential which, for non-zero moduli expectation values, generate moduli dependent mu-terms of the form H Hbar. It is found that these interactions are subject to two very restrictive selection rules, each arising from a Leray spectral sequence, which greatly reduce the number of moduli that can couple to Higgs-Higgs conjugate fields. We apply our formalism to a specific heterotic standard model vacuum. The non-vanishing cubic interactions phi H Hbar are explicitly computed in this context and shown to contain only four of the nineteen vector bundle moduli.
Stable, holomorphic vector bundles are constructed on an torus fibered, non-simply connected Cala... more Stable, holomorphic vector bundles are constructed on an torus fibered, non-simply connected Calabi-Yau threefold using the method of bundle extensions. Since the manifold is multiply connected, we work with equivariant bundles on the elliptically fibered covering space. The cohomology groups of the vector bundle, which yield the low energy spectrum, are computed using the Leray spectral sequence and fit the requirements of particle phenomenology. The physical properties of these vacua were discussed previously. In this paper, we systematically compute all relevant cohomology groups and explicitly prove the existence of the necessary vector bundle extensions. All mathematical details are explained in a pedagogical way, providing the technical framework for constructing heterotic standard model vacua.
Physics Letters B, 2005
Within the context of the E 8 × E 8 heterotic superstring compactified on a smooth Calabi-Yau thr... more Within the context of the E 8 × E 8 heterotic superstring compactified on a smooth Calabi-Yau threefold with an SU (4) gauge instanton, we show the existence of simple, realistic N = 1 supersymmetric vacua that are compatible with low energy particle physics. The observable sector of these vacua has gauge group SU (3) C × SU (2) L × U (1) Y × U (1) B−L , three families of quarks and leptons, each with an additional right-handed neutrino, two Higgs-Higgs conjugate pairs, a small number of uncharged moduli and no exotic matter. The hidden sector contains non-Abelian gauge fields and moduli. In the strong coupling case there is no exotic matter, whereas for weak coupling there are a small number of additional matter multiplets in the hidden sector. The construction exploits a mechanism for "splitting" multiplets. The minimal nature and rarity of these vacua suggest the possible theoretical and experimental relevance of spontaneously broken U (1) B−L gauge symmetry and two Higgs-Higgs conjugate pairs. The U (1) B−L symmetry helps to naturally suppress the rate of nucleon decay.
Journal of High Energy Physics, 2004
Techniques are presented for computing the cohomology of stable, holomorphic vector bundles over ... more Techniques are presented for computing the cohomology of stable, holomorphic vector bundles over elliptically fibered Calabi-Yau threefolds. These cohomology groups explicitly determine the spectrum of the low energy, four-dimensional theory. Generic points in vector bundle moduli space manifest an identical spectrum. However, it is shown that on subsets of moduli space of co-dimension one or higher, the spectrum can abruptly jump to many different values. Both analytic and numerical data illustrating this phenomenon are presented. This result opens the possibility of tunneling or phase transitions between different particle spectra in the same heterotic compactification. In the course of this discussion, a classification of SU(5) GUT theories within a specific context is presented.
Physics Letters B, 2003
In this paper we continue the investigation, within the context of the Dijkgraaf-Vafa Programme, ... more In this paper we continue the investigation, within the context of the Dijkgraaf-Vafa Programme, of Seiberg duality in matrix models as initiated in hep-th/0211202, by allowing degenerate mass deformations. In this case, there are some massless fields which remain and the theory has a moduli space. With this illustrative example, we propose a general methodology for performing the relevant matrix model integrations and addressing the corresponding field theories which have non-trivial IR behaviour, and which may or may not have tree-level superpotentials.
Dimer models are 2-dimensional combinatorial systems that have been shown to encode the gauge gro... more Dimer models are 2-dimensional combinatorial systems that have been shown to encode the gauge groups, matter content and tree-level superpotential of the world-volume quiver gauge theories obtained by placing D3-branes at the tip of a singular toric Calabi-Yau cone. In particular the dimer graph is dual to the quiver graph. However, the string theoretic explanation of this was unclear. In this paper we use mirror symmetry to shed light on this: the dimer models live on a T^2 subspace of the T^3 fiber that is involved in mirror symmetry and is wrapped by D6-branes. These D6-branes are mirror to the D3-branes at the singular point, and geometrically encode the same quiver theory on their world-volume.
We initiate a systematic investigation of the space of 2+1 dimensional quiver gauge theories, emp... more We initiate a systematic investigation of the space of 2+1 dimensional quiver gauge theories, emphasising a succinct "forward algorithm". Few "order parametres" are introduced such as the number of terms in the superpotential and the number of gauge groups. Starting with two terms in the superpotential, we find a generating function, with interesting geometric interpretation, which counts the number of inequivalent theories for a given number of gauge groups and fields. We demonstratively list these theories for some low numbers thereof. Furthermore, we show how these theories arise from M2-branes probing toric Calabi-Yau 4-folds by explicitly obtaining the toric data of the vacuum moduli space. By observing equivalences of the vacua between markedly different theories, we see a new emergence of "toric duality".
We compute the NSVZ beta functions for N = 1 four-dimensional quiver theories arising from D-bran... more We compute the NSVZ beta functions for N = 1 four-dimensional quiver theories arising from D-brane probes on singularities, complete with anomalous dimensions, for a large set of phases in the corresponding duality tree. While these beta functions are zero for D-brane probes, they are non-zero in the presence of fractional branes. As a result there is a non-trivial RG behavior. We apply this running of gauge couplings to some toric singularities such as the cones over Hirzebruch and del Pezzo surfaces. We observe the emergence in string theory, of ``Duality Walls,'' a finite energy scale at which the number of degrees of freedom becomes infinite, and beyond which Seiberg duality does not proceed. We also identify certain quiver symmetries as T-duality-like actions in the dual holographic theory.
Nuclear Physics B, 2001
We discuss examples of D-branes probing toric singularities, and the computation of their world-v... more We discuss examples of D-branes probing toric singularities, and the computation of their world-volume gauge theories from the geometric data of the singularities. We consider several such examples of D-branes on partial resolutions of the orbifolds C
Journal of High Energy Physics, 2008
The full moduli space M of a class of N = 1 supersymmetric gauge theories is studied. For gauge t... more The full moduli space M of a class of N = 1 supersymmetric gauge theories is studied. For gauge theories living on a stack of D3-branes at Calabi-Yau singularities X , M is a combination of the mesonic and baryonic branches. In consonance with the mathematical literature, the single brane moduli space is called the master space F ♭ . Illustrating with a host of explicit examples, we exhibit many algebro-geometric properties of the master space such as when F ♭ is toric Calabi-Yau, behaviour of its Hilbert series, its irreducible components and its symmetries. In conjunction with the plethystic programme, we investigate the counting of BPS gauge invariants, baryonic and mesonic, using the geometry of F ♭ and show how its refined Hilbert series not only engenders the generating functions for the counting but also beautifully encode "hidden" global symmetries of the gauge theory which manifest themselves as symmetries of the complete moduli space M for N number of branes. * forcella@sissa.it † a.hanany@imperial.ac.uk, hanany@physics.technion.ac.il ‡ hey@maths.ox.ac.uk
Journal of High Energy Physics, 2002
We calculate the spectrum of the matrix M' of Neumann coefficients of the Witten vertex, expresse... more We calculate the spectrum of the matrix M' of Neumann coefficients of the Witten vertex, expressed in the oscillator basis including the zero-mode a_0. We find that in addition to the known continuous spectrum inside [-1/3,0) of the matrix M without the zero-modes, there is also an additional eigenvalue inside (0,1). For every eigenvalue, there is a pair of eigenvectors, a twist-even and a twist-odd. We give analytically these eigenvectors as well as the generating function for their components. Also, we have found an interesting critical parameter b_0 = 8 ln 2 on which the forms of the eigenvectors depend.
Journal of High Energy Physics, 2003
We develop an unhiggsing procedure for finding the D-brane probe world volume gauge theory for bl... more We develop an unhiggsing procedure for finding the D-brane probe world volume gauge theory for blowups of geometries whose gauge theory data are known. As specific applications we unhiggs the well-studied theories for the cone over the third del Pezzo surface. We arrive at what we call pseudo del Pezzos and these will constitute a first step toward the understanding of higher, non toric del Pezzos. Moreover, our methods and results give further support for toric duality as well as obtaining superpotentials from global symmetry considerations.
Journal of High Energy Physics, 2001
We use field theory and brane diamond techniques to demonstrate that Toric Duality is Seiberg dua... more We use field theory and brane diamond techniques to demonstrate that Toric Duality is Seiberg duality. This resolves the puzzle concerning the physical meaning of Toric Duality as proposed in our earlier work. Furthermore, using this strong connection we arrive at three new phases which can not be thus far obtained by the so-called "Inverse Algorithm" applied to partial resolution of C 3 /(Z Z 3 × Z Z 3 ). The standing proposals of Seiberg duality as diamond duality in the work by Aganagic-Karch-Lüst-Miemiec are strongly supported and new diamond configurations for these singularities are obtained as a byproduct. We also make some remarks about the relationships between Seiberg duality and Picard-Lefschetz monodromy.
Journal of High Energy Physics, 2002
in the construction for world volume theories of D-branes probing arbitrary toric singularities. ... more in the construction for world volume theories of D-branes probing arbitrary toric singularities. This duality will be seen to be due to certain permutation symmetries of multiplicities in the gauged linear sigma model fields. To this symmetry we shall refer as ``multiplicity symmetry.'' We present beautiful combinatorial properties of these multiplicities and rederive all known cases of torically dual theories under this new light. We also initiate an understanding of why such multiplicity symmetry naturally leads to monodromy and Seiberg duality. Furthermore we discuss certain ``flavor'' and ``node'' symmetries of the quiver and superpotential and how they are intimately related to the isometry of the background geometry, as well as how in certain cases complicated superpotentials can be derived by observations of the symmetries alone.
Journal of High Energy Physics, 2001
We show that the triviality of the entire cohomology of the new BRST operator Q around the tachyo... more We show that the triviality of the entire cohomology of the new BRST operator Q around the tachyon vacuum is equivalent to the Q-exactness of the identity I of the star-algebra. We use level truncation to show that as the level is increased, the identity becomes more accurately Q-exact. We carry our computations up to level nine, where an accuracy of 3% is attained. Our work supports, under a new light, Sen's conjecture concerning the absence of open string degrees of freedom around the tachyon vacuum. As a by-product, a new and simple expression for I in terms of Virasoro operators is found.
Physical Review D, 2003
We obtain explicit formulas for the Neumann coefficients and associated quantities that appear in... more We obtain explicit formulas for the Neumann coefficients and associated quantities that appear in the three-string vertex for type IIB string theory in a plane-wave background, for any value of the mass parameter mu. The derivation involves constructing the inverse of a certain infinite-dimensional matrix, in terms of which the Neumann coefficients previously had been written only implicitly. We derive asymptotic expansions for large mu and find unexpectedly simple results, which are valid to all orders in 1/mu. Using BMN duality, these give predictions for certain gauge theory quantities to all orders in the modified 't Hooft coupling lambda'. A specific example is presented.
Physical Review D, 2004
We investigate the general features of renormalization group flows near superconformal fixed poin... more We investigate the general features of renormalization group flows near superconformal fixed points of four dimensional N=1 supersymmetric gauge theories with gravity duals. The gauge theories we study arise as the world-volume theory on a set of D-branes at a Calabi-Yau singularity where a del Pezzo surface shrinks to zero size. Based mainly on field theory analysis, we find evidence that such flows are often chaotic and contain exotic features such as duality walls. For a gauge theory where the del Pezzo is the Hirzebruch zero surface, the dependence of the duality wall height on the couplings at some point in the cascade has a self-similar fractal structure. For a gauge theory dual to CP^2 blown up at a point, we find periodic and quasi-periodic behavior for the gauge theory couplings that does not violate the a-conjecture. Finally, we construct supergravity duals for these del Pezzos that match our field theory beta functions.
Fortschritte Der Physik-progress of Physics, 2006
Within the context of the E8 × E8 heterotic superstring compactified on a smooth Calabi-Yau three... more Within the context of the E8 × E8 heterotic superstring compactified on a smooth Calabi-Yau threefold with an SU(4) gauge instanton, we show the existence of simple, realistic N = 1 supersymmetric vacua that are compatible with low energy particle physics. The observable sector of these vacua has gauge group SU(3)C × SU(2)L × U(1)Y × U(1)B-L, three families of quarks and leptons, each with an additional right-handed neutrino, two Higgs-Higgs conjugate pairs, a small number of uncharged moduli and no exotic matter.
Physics Letters B, 2004
Explicit methods are presented for computing the cohomology of stable, holomorphic vector bundles... more Explicit methods are presented for computing the cohomology of stable, holomorphic vector bundles on elliptically fibered Calabi-Yau threefolds. The complete particle spectrum of the low-energy, four-dimensional theory is specified by the dimensions of specific cohomology groups. The spectrum is shown to depend on the choice of vector bundle moduli, jumping up from a generic minimal result to attain many higher values on subspaces of co-dimension one or higher in the moduli space. An explicit example is presented within the context of a heterotic vacuum corresponding to an SU (5) GUT in four-dimensions. *
Journal of High Energy Physics, 2006
We show the existence of realistic vacua in string theory whose observable sector has exactly the... more We show the existence of realistic vacua in string theory whose observable sector has exactly the matter content of the MSSM. This is achieved by compactifying the E_8 x E_8 heterotic superstring on a smooth Calabi-Yau threefold with an SU(4) gauge instanton and a Z_3 x Z_3 Wilson line. Specifically, the observable sector is N=1 supersymmetric with gauge group SU(3)_C x SU(2)_L x U(1)_Y x U(1)_{B-L}, three families of quarks and leptons, each family with a right-handed neutrino, and one Higgs-Higgs conjugate pair. Importantly, there are no extra vector-like pairs and no exotic matter in the zero mode spectrum. There are, in addition, 6 geometric moduli and 13 gauge instanton moduli in the observable sector. The holomorphic SU(4) vector bundle of the observable sector is slope-stable.
Journal of High Energy Physics, 2006
In this paper, we present a formalism for computing the non-vanishing Higgs mu-terms in a heterot... more In this paper, we present a formalism for computing the non-vanishing Higgs mu-terms in a heterotic standard model. This is accomplished by calculating the cubic product of the cohomology groups associated with the vector bundle moduli (phi), Higgs (H) and Higgs conjugate (Hbar) superfields. This leads to terms proportional to phi H Hbar in the low energy superpotential which, for non-zero moduli expectation values, generate moduli dependent mu-terms of the form H Hbar. It is found that these interactions are subject to two very restrictive selection rules, each arising from a Leray spectral sequence, which greatly reduce the number of moduli that can couple to Higgs-Higgs conjugate fields. We apply our formalism to a specific heterotic standard model vacuum. The non-vanishing cubic interactions phi H Hbar are explicitly computed in this context and shown to contain only four of the nineteen vector bundle moduli.
Stable, holomorphic vector bundles are constructed on an torus fibered, non-simply connected Cala... more Stable, holomorphic vector bundles are constructed on an torus fibered, non-simply connected Calabi-Yau threefold using the method of bundle extensions. Since the manifold is multiply connected, we work with equivariant bundles on the elliptically fibered covering space. The cohomology groups of the vector bundle, which yield the low energy spectrum, are computed using the Leray spectral sequence and fit the requirements of particle phenomenology. The physical properties of these vacua were discussed previously. In this paper, we systematically compute all relevant cohomology groups and explicitly prove the existence of the necessary vector bundle extensions. All mathematical details are explained in a pedagogical way, providing the technical framework for constructing heterotic standard model vacua.
Physics Letters B, 2005
Within the context of the E 8 × E 8 heterotic superstring compactified on a smooth Calabi-Yau thr... more Within the context of the E 8 × E 8 heterotic superstring compactified on a smooth Calabi-Yau threefold with an SU (4) gauge instanton, we show the existence of simple, realistic N = 1 supersymmetric vacua that are compatible with low energy particle physics. The observable sector of these vacua has gauge group SU (3) C × SU (2) L × U (1) Y × U (1) B−L , three families of quarks and leptons, each with an additional right-handed neutrino, two Higgs-Higgs conjugate pairs, a small number of uncharged moduli and no exotic matter. The hidden sector contains non-Abelian gauge fields and moduli. In the strong coupling case there is no exotic matter, whereas for weak coupling there are a small number of additional matter multiplets in the hidden sector. The construction exploits a mechanism for "splitting" multiplets. The minimal nature and rarity of these vacua suggest the possible theoretical and experimental relevance of spontaneously broken U (1) B−L gauge symmetry and two Higgs-Higgs conjugate pairs. The U (1) B−L symmetry helps to naturally suppress the rate of nucleon decay.
Journal of High Energy Physics, 2004
Techniques are presented for computing the cohomology of stable, holomorphic vector bundles over ... more Techniques are presented for computing the cohomology of stable, holomorphic vector bundles over elliptically fibered Calabi-Yau threefolds. These cohomology groups explicitly determine the spectrum of the low energy, four-dimensional theory. Generic points in vector bundle moduli space manifest an identical spectrum. However, it is shown that on subsets of moduli space of co-dimension one or higher, the spectrum can abruptly jump to many different values. Both analytic and numerical data illustrating this phenomenon are presented. This result opens the possibility of tunneling or phase transitions between different particle spectra in the same heterotic compactification. In the course of this discussion, a classification of SU(5) GUT theories within a specific context is presented.
Physics Letters B, 2003
In this paper we continue the investigation, within the context of the Dijkgraaf-Vafa Programme, ... more In this paper we continue the investigation, within the context of the Dijkgraaf-Vafa Programme, of Seiberg duality in matrix models as initiated in hep-th/0211202, by allowing degenerate mass deformations. In this case, there are some massless fields which remain and the theory has a moduli space. With this illustrative example, we propose a general methodology for performing the relevant matrix model integrations and addressing the corresponding field theories which have non-trivial IR behaviour, and which may or may not have tree-level superpotentials.
Dimer models are 2-dimensional combinatorial systems that have been shown to encode the gauge gro... more Dimer models are 2-dimensional combinatorial systems that have been shown to encode the gauge groups, matter content and tree-level superpotential of the world-volume quiver gauge theories obtained by placing D3-branes at the tip of a singular toric Calabi-Yau cone. In particular the dimer graph is dual to the quiver graph. However, the string theoretic explanation of this was unclear. In this paper we use mirror symmetry to shed light on this: the dimer models live on a T^2 subspace of the T^3 fiber that is involved in mirror symmetry and is wrapped by D6-branes. These D6-branes are mirror to the D3-branes at the singular point, and geometrically encode the same quiver theory on their world-volume.
We initiate a systematic investigation of the space of 2+1 dimensional quiver gauge theories, emp... more We initiate a systematic investigation of the space of 2+1 dimensional quiver gauge theories, emphasising a succinct "forward algorithm". Few "order parametres" are introduced such as the number of terms in the superpotential and the number of gauge groups. Starting with two terms in the superpotential, we find a generating function, with interesting geometric interpretation, which counts the number of inequivalent theories for a given number of gauge groups and fields. We demonstratively list these theories for some low numbers thereof. Furthermore, we show how these theories arise from M2-branes probing toric Calabi-Yau 4-folds by explicitly obtaining the toric data of the vacuum moduli space. By observing equivalences of the vacua between markedly different theories, we see a new emergence of "toric duality".
We compute the NSVZ beta functions for N = 1 four-dimensional quiver theories arising from D-bran... more We compute the NSVZ beta functions for N = 1 four-dimensional quiver theories arising from D-brane probes on singularities, complete with anomalous dimensions, for a large set of phases in the corresponding duality tree. While these beta functions are zero for D-brane probes, they are non-zero in the presence of fractional branes. As a result there is a non-trivial RG behavior. We apply this running of gauge couplings to some toric singularities such as the cones over Hirzebruch and del Pezzo surfaces. We observe the emergence in string theory, of ``Duality Walls,'' a finite energy scale at which the number of degrees of freedom becomes infinite, and beyond which Seiberg duality does not proceed. We also identify certain quiver symmetries as T-duality-like actions in the dual holographic theory.
Nuclear Physics B, 2001
We discuss examples of D-branes probing toric singularities, and the computation of their world-v... more We discuss examples of D-branes probing toric singularities, and the computation of their world-volume gauge theories from the geometric data of the singularities. We consider several such examples of D-branes on partial resolutions of the orbifolds C
Journal of High Energy Physics, 2008
The full moduli space M of a class of N = 1 supersymmetric gauge theories is studied. For gauge t... more The full moduli space M of a class of N = 1 supersymmetric gauge theories is studied. For gauge theories living on a stack of D3-branes at Calabi-Yau singularities X , M is a combination of the mesonic and baryonic branches. In consonance with the mathematical literature, the single brane moduli space is called the master space F ♭ . Illustrating with a host of explicit examples, we exhibit many algebro-geometric properties of the master space such as when F ♭ is toric Calabi-Yau, behaviour of its Hilbert series, its irreducible components and its symmetries. In conjunction with the plethystic programme, we investigate the counting of BPS gauge invariants, baryonic and mesonic, using the geometry of F ♭ and show how its refined Hilbert series not only engenders the generating functions for the counting but also beautifully encode "hidden" global symmetries of the gauge theory which manifest themselves as symmetries of the complete moduli space M for N number of branes. * forcella@sissa.it † a.hanany@imperial.ac.uk, hanany@physics.technion.ac.il ‡ hey@maths.ox.ac.uk
Journal of High Energy Physics, 2002
We calculate the spectrum of the matrix M' of Neumann coefficients of the Witten vertex, expresse... more We calculate the spectrum of the matrix M' of Neumann coefficients of the Witten vertex, expressed in the oscillator basis including the zero-mode a_0. We find that in addition to the known continuous spectrum inside [-1/3,0) of the matrix M without the zero-modes, there is also an additional eigenvalue inside (0,1). For every eigenvalue, there is a pair of eigenvectors, a twist-even and a twist-odd. We give analytically these eigenvectors as well as the generating function for their components. Also, we have found an interesting critical parameter b_0 = 8 ln 2 on which the forms of the eigenvectors depend.
Journal of High Energy Physics, 2003
We develop an unhiggsing procedure for finding the D-brane probe world volume gauge theory for bl... more We develop an unhiggsing procedure for finding the D-brane probe world volume gauge theory for blowups of geometries whose gauge theory data are known. As specific applications we unhiggs the well-studied theories for the cone over the third del Pezzo surface. We arrive at what we call pseudo del Pezzos and these will constitute a first step toward the understanding of higher, non toric del Pezzos. Moreover, our methods and results give further support for toric duality as well as obtaining superpotentials from global symmetry considerations.
Journal of High Energy Physics, 2001
We use field theory and brane diamond techniques to demonstrate that Toric Duality is Seiberg dua... more We use field theory and brane diamond techniques to demonstrate that Toric Duality is Seiberg duality. This resolves the puzzle concerning the physical meaning of Toric Duality as proposed in our earlier work. Furthermore, using this strong connection we arrive at three new phases which can not be thus far obtained by the so-called "Inverse Algorithm" applied to partial resolution of C 3 /(Z Z 3 × Z Z 3 ). The standing proposals of Seiberg duality as diamond duality in the work by Aganagic-Karch-Lüst-Miemiec are strongly supported and new diamond configurations for these singularities are obtained as a byproduct. We also make some remarks about the relationships between Seiberg duality and Picard-Lefschetz monodromy.
Journal of High Energy Physics, 2002
in the construction for world volume theories of D-branes probing arbitrary toric singularities. ... more in the construction for world volume theories of D-branes probing arbitrary toric singularities. This duality will be seen to be due to certain permutation symmetries of multiplicities in the gauged linear sigma model fields. To this symmetry we shall refer as ``multiplicity symmetry.'' We present beautiful combinatorial properties of these multiplicities and rederive all known cases of torically dual theories under this new light. We also initiate an understanding of why such multiplicity symmetry naturally leads to monodromy and Seiberg duality. Furthermore we discuss certain ``flavor'' and ``node'' symmetries of the quiver and superpotential and how they are intimately related to the isometry of the background geometry, as well as how in certain cases complicated superpotentials can be derived by observations of the symmetries alone.
Journal of High Energy Physics, 2001
We show that the triviality of the entire cohomology of the new BRST operator Q around the tachyo... more We show that the triviality of the entire cohomology of the new BRST operator Q around the tachyon vacuum is equivalent to the Q-exactness of the identity I of the star-algebra. We use level truncation to show that as the level is increased, the identity becomes more accurately Q-exact. We carry our computations up to level nine, where an accuracy of 3% is attained. Our work supports, under a new light, Sen's conjecture concerning the absence of open string degrees of freedom around the tachyon vacuum. As a by-product, a new and simple expression for I in terms of Virasoro operators is found.