gabor Armoni | Swansea University (original) (raw)

Papers by gabor Armoni

Journal of High Energy Physics, 1999

We study five dimensional non critical type 0 string theory and its correspondence to non supersy... more We study five dimensional non critical type 0 string theory and its correspondence to non supersymmetric Yang Mills theory in four dimensions. We solve the equations of motion of the low energy effective action and identify a class of solutions that translates into a confining behavior in the IR region of the dual gauge theories. In particular we identify a setup which is dual to pure SU (N ) Yang-Mills theory. Possible flows of the solutions to the UV region are discussed. The validity of the solutions and potential sub-leading string corrections are also discussed.

We consider "Orientifold field theories", namely SU (N ) gauge theories with Dirac fermions in th... more We consider "Orientifold field theories", namely SU (N ) gauge theories with Dirac fermions in the two-index representation at high temperature. When N is even these theories exhibit a spontaneously broken Z 2 centre symmetry. We study aspects of the domain wall that interpolates between the two vacua of the theory. In particular we calculate its tension to two-loop order. We compare its tension to the corresponding domain wall in a SU (N ) gauge theory with adjoint fermions and find an agreement at large-N , as expected from planar equivalence between the two theories. Moreover, we provide a nonperturbative proof for the coincidence of the tensions at large-N . We also discuss the vacuum structure of the theory when the fermion is given a large mass and argue that there exist N − 2 metastable vacua. We calculate the lifetime of those vacua in the thin wall approximation.

We use type IIB brane configurations which were recently suggested by Hanany and Zaffaroni to stu... more We use type IIB brane configurations which were recently suggested by Hanany and Zaffaroni to study four dimensional N=1 supersymmetric gauge theories. We calculate the one loop beta function and realize Seiberg's duality using a particular configuration. We also comment on the anomaly cancelation condition in the case of chiral theories and the beta function in the case of chiral and SO/Sp theories.

We discuss the Seiberg-Witten solution of the non-commutative N = 2 U (N ) SYM model. The solutio... more We discuss the Seiberg-Witten solution of the non-commutative N = 2 U (N ) SYM model. The solution is described in terms of the ordinary Seiberg-Witten curve of the SU (N ) theory plus an additional free U (1). Hence, at the two-derivative approximation the theory flows to the ordinary commutative theory in the infra-red (k <

We analyze the possibility of a spontaneous breaking of C-invariance in gauge theories with fermi... more We analyze the possibility of a spontaneous breaking of C-invariance in gauge theories with fermions in vector-like -but otherwise generic -representations of the gauge group. QCD, supersymmetric Yang-Mills theory, and orientifold field theories, all belong to this class. We argue that charge conjugation is not spontaneously broken as long as Lorentz invariance is maintained. Uniqueness of the vacuum state in pure Yang-Mills theory (without fermions) and convergence of the expansion in fermion loops are key ingredients. The fact that C-invariance is conserved has an interesting application to our proof of planar equivalence between supersymmetric Yang-Mills theory and orientifold field theory on R 4 , since it allows the use of charge conjugation to connect the large-N limit of Wilson loops in different representations.

... t Hooft model Nf = 1 is exactly solvable, the multi-flavor case Nf > 1 is not solvable mod... more ... t Hooft model Nf = 1 is exactly solvable, the multi-flavor case Nf > 1 is not solvable model even in the Veneziano limit when both Nc and Nf are taken to infinity (with a fixed ratio), since paircreation and annihilation is ... 336 Adi Armoni, Yitzhak Frishman, and Jacob Sonnenschein ...

ABSTRACT We consider the dynamics of a strongly coupled SU(N) chiral gauge theory. By using its l... more ABSTRACT We consider the dynamics of a strongly coupled SU(N) chiral gauge theory. By using its large-N equivalence with N=1 super-Yang-Mills theory we find the vacuum structure of the former. We also consider its finite-N dynamics.

We consider non-supersymmetric large N orientifold field theories. Specifically, we discuss a gau... more We consider non-supersymmetric large N orientifold field theories. Specifically, we discuss a gauge theory with a Dirac fermion in the anti-symmetric tensor representation. We argue that, at large N and in a large part of its bosonic sector, this theory is non-perturbatively equivalent to N = 1 SYM, so that exact results established in the latter (parent) theory also hold in the daughter orientifold theory. In particular, the nonsupersymmetric theory has an exactly calculable bifermion condensate, exactly degenerate parity doublets, and a vanishing cosmological constant (all this to leading order in 1/N ). To be more precise, the gauge groups are almost the same. The U(1) factor completely decouples in the parent theory, while it does not decouple in the daughter one. Moreover, in the former theory the Z k center of the gauge group acts trivially while in the latter one it is only Z 2 that acts trivially. These distinctions are unimportant in the large-N limit.

We study the correlators of two circular Wilson loops of different radii at strong coupling. In o... more We study the correlators of two circular Wilson loops of different radii at strong coupling. In our setup one Wilson loop is located inside the other. We use holography to calculate the connected two-point function. Both an AdS background and a confining background are considered. As the computation for the confining case cannot be carried out analytically we solve the problem numerically. In the AdS case our results agree with similar holographic calculations. In the case of a confining background we find an asymptotic area law, in agreement with the result of the lattice strong coupling expansion. We also elaborate on the subtle issue of the interplay between connected and disconnected string worldsheets.

We discuss a nonperturbative relation for orientifold parent/daughter pairs of supersymmetric the... more We discuss a nonperturbative relation for orientifold parent/daughter pairs of supersymmetric theories with an arbitrary tree-level superpotential. We show that super-Yang-Mills (SYM) theory with matter in the adjoint representation at N → ∞, is equivalent to a SYM theory with matter in the antisymmetric representation and a related superpotential. The gauge symmetry breaking patterns match in these theories too. The moduli spaces in the limiting case of a vanishing superpotential are also discussed. Finally we argue that there is an exact mapping between the effective superpotentials of two finite-N theories belonging to an orientifold pair.

Domain walls in supersymmetric Yang-Mills are BPS configurations which preserve two supercharges ... more Domain walls in supersymmetric Yang-Mills are BPS configurations which preserve two supercharges of the parent theory and so their tensions are known exactly. On the other hand, they have been described as D-branes for the confining string. This leads to a description of their collective dynamics in terms of a 2 + 1dimensional gauge theory with two supersymmetries and a Chern-Simons term. We show that this open string description can capture the qualitative behaviour of the forces between the domain walls for an arbitrary configuration of n walls at leading order in 1/N, extending earlier calculations for two walls. The potential admits a supersymmetric bound state when the n walls are all coincident and asymptotes to a constant at large separation with an n dependence which agrees perfectly with the exact tension formula.

Massless QCD 2 is dominated by classical configurations in the large N f limit. We use this obser... more Massless QCD 2 is dominated by classical configurations in the large N f limit. We use this observation to study the theory by finding solutions to equations of motion, which are the non-Abelian generalization of the Schwinger equation. We find that the spectrum consists of massive mesons with M 2 = e 2 N f 2π which correspond to Abelian solutions. We generalize previously discovered non-Abelian solutions and discuss their interpretation. We prove a no-go theorem ruling out the existence of soliton solutions. Thus the semi-classical approximation shows no baryons in the case of massless quarks, a result derived before in the strong-coupling limit only. 1

In pure N = 1 supersymmetric Yang-Mills with gauge group SU(N), the domain walls which separate t... more In pure N = 1 supersymmetric Yang-Mills with gauge group SU(N), the domain walls which separate the N vacua have been argued, on the basis of string theory realizations, to be D-branes for the confining string. In a certain limit, this means that a configuration of k parallel domain walls is described by a 2 + 1dimensional U(k) gauge theory. This theory has been identified by Acharya and Vafa as the U(k) gauge theory with 4 supercharges broken by a Chern-Simons term of level N in such a way that 2 supercharges are preserved. We argue further that the gauge coupling of the domain wall gauge theory goes like g 2 ∼ Λ/N, for large N. In the case of two domain walls, we show that the U(2) world-volume theory generates a quadratic potential on the Coulomb branch at two loops in perturbation theory which is consistent with there being a supersymmetric bound state of the two wall system. A mass gap of order Λ/N is generated around the supersymmetric minimum and we estimate the size of the bound-state to be order Λ/ √ N . At large distance the potential reaches a constant that can qualitatively account for the binding energy of the two walls even though stringy effects are not, strictly speaking, decoupled.

Journal of High Energy Physics, 1999

We study five dimensional non critical type 0 string theory and its correspondence to non supersy... more We study five dimensional non critical type 0 string theory and its correspondence to non supersymmetric Yang Mills theory in four dimensions. We solve the equations of motion of the low energy effective action and identify a class of solutions that translates into a confining behavior in the IR region of the dual gauge theories. In particular we identify a setup which is dual to pure SU (N ) Yang-Mills theory. Possible flows of the solutions to the UV region are discussed. The validity of the solutions and potential sub-leading string corrections are also discussed.

We consider "Orientifold field theories", namely SU (N ) gauge theories with Dirac fermions in th... more We consider "Orientifold field theories", namely SU (N ) gauge theories with Dirac fermions in the two-index representation at high temperature. When N is even these theories exhibit a spontaneously broken Z 2 centre symmetry. We study aspects of the domain wall that interpolates between the two vacua of the theory. In particular we calculate its tension to two-loop order. We compare its tension to the corresponding domain wall in a SU (N ) gauge theory with adjoint fermions and find an agreement at large-N , as expected from planar equivalence between the two theories. Moreover, we provide a nonperturbative proof for the coincidence of the tensions at large-N . We also discuss the vacuum structure of the theory when the fermion is given a large mass and argue that there exist N − 2 metastable vacua. We calculate the lifetime of those vacua in the thin wall approximation.

We use type IIB brane configurations which were recently suggested by Hanany and Zaffaroni to stu... more We use type IIB brane configurations which were recently suggested by Hanany and Zaffaroni to study four dimensional N=1 supersymmetric gauge theories. We calculate the one loop beta function and realize Seiberg's duality using a particular configuration. We also comment on the anomaly cancelation condition in the case of chiral theories and the beta function in the case of chiral and SO/Sp theories.

We discuss the Seiberg-Witten solution of the non-commutative N = 2 U (N ) SYM model. The solutio... more We discuss the Seiberg-Witten solution of the non-commutative N = 2 U (N ) SYM model. The solution is described in terms of the ordinary Seiberg-Witten curve of the SU (N ) theory plus an additional free U (1). Hence, at the two-derivative approximation the theory flows to the ordinary commutative theory in the infra-red (k <

We analyze the possibility of a spontaneous breaking of C-invariance in gauge theories with fermi... more We analyze the possibility of a spontaneous breaking of C-invariance in gauge theories with fermions in vector-like -but otherwise generic -representations of the gauge group. QCD, supersymmetric Yang-Mills theory, and orientifold field theories, all belong to this class. We argue that charge conjugation is not spontaneously broken as long as Lorentz invariance is maintained. Uniqueness of the vacuum state in pure Yang-Mills theory (without fermions) and convergence of the expansion in fermion loops are key ingredients. The fact that C-invariance is conserved has an interesting application to our proof of planar equivalence between supersymmetric Yang-Mills theory and orientifold field theory on R 4 , since it allows the use of charge conjugation to connect the large-N limit of Wilson loops in different representations.

... t Hooft model Nf = 1 is exactly solvable, the multi-flavor case Nf > 1 is not solvable mod... more ... t Hooft model Nf = 1 is exactly solvable, the multi-flavor case Nf > 1 is not solvable model even in the Veneziano limit when both Nc and Nf are taken to infinity (with a fixed ratio), since paircreation and annihilation is ... 336 Adi Armoni, Yitzhak Frishman, and Jacob Sonnenschein ...

ABSTRACT We consider the dynamics of a strongly coupled SU(N) chiral gauge theory. By using its l... more ABSTRACT We consider the dynamics of a strongly coupled SU(N) chiral gauge theory. By using its large-N equivalence with N=1 super-Yang-Mills theory we find the vacuum structure of the former. We also consider its finite-N dynamics.

We consider non-supersymmetric large N orientifold field theories. Specifically, we discuss a gau... more We consider non-supersymmetric large N orientifold field theories. Specifically, we discuss a gauge theory with a Dirac fermion in the anti-symmetric tensor representation. We argue that, at large N and in a large part of its bosonic sector, this theory is non-perturbatively equivalent to N = 1 SYM, so that exact results established in the latter (parent) theory also hold in the daughter orientifold theory. In particular, the nonsupersymmetric theory has an exactly calculable bifermion condensate, exactly degenerate parity doublets, and a vanishing cosmological constant (all this to leading order in 1/N ). To be more precise, the gauge groups are almost the same. The U(1) factor completely decouples in the parent theory, while it does not decouple in the daughter one. Moreover, in the former theory the Z k center of the gauge group acts trivially while in the latter one it is only Z 2 that acts trivially. These distinctions are unimportant in the large-N limit.

We study the correlators of two circular Wilson loops of different radii at strong coupling. In o... more We study the correlators of two circular Wilson loops of different radii at strong coupling. In our setup one Wilson loop is located inside the other. We use holography to calculate the connected two-point function. Both an AdS background and a confining background are considered. As the computation for the confining case cannot be carried out analytically we solve the problem numerically. In the AdS case our results agree with similar holographic calculations. In the case of a confining background we find an asymptotic area law, in agreement with the result of the lattice strong coupling expansion. We also elaborate on the subtle issue of the interplay between connected and disconnected string worldsheets.

We discuss a nonperturbative relation for orientifold parent/daughter pairs of supersymmetric the... more We discuss a nonperturbative relation for orientifold parent/daughter pairs of supersymmetric theories with an arbitrary tree-level superpotential. We show that super-Yang-Mills (SYM) theory with matter in the adjoint representation at N → ∞, is equivalent to a SYM theory with matter in the antisymmetric representation and a related superpotential. The gauge symmetry breaking patterns match in these theories too. The moduli spaces in the limiting case of a vanishing superpotential are also discussed. Finally we argue that there is an exact mapping between the effective superpotentials of two finite-N theories belonging to an orientifold pair.

Domain walls in supersymmetric Yang-Mills are BPS configurations which preserve two supercharges ... more Domain walls in supersymmetric Yang-Mills are BPS configurations which preserve two supercharges of the parent theory and so their tensions are known exactly. On the other hand, they have been described as D-branes for the confining string. This leads to a description of their collective dynamics in terms of a 2 + 1dimensional gauge theory with two supersymmetries and a Chern-Simons term. We show that this open string description can capture the qualitative behaviour of the forces between the domain walls for an arbitrary configuration of n walls at leading order in 1/N, extending earlier calculations for two walls. The potential admits a supersymmetric bound state when the n walls are all coincident and asymptotes to a constant at large separation with an n dependence which agrees perfectly with the exact tension formula.

Massless QCD 2 is dominated by classical configurations in the large N f limit. We use this obser... more Massless QCD 2 is dominated by classical configurations in the large N f limit. We use this observation to study the theory by finding solutions to equations of motion, which are the non-Abelian generalization of the Schwinger equation. We find that the spectrum consists of massive mesons with M 2 = e 2 N f 2π which correspond to Abelian solutions. We generalize previously discovered non-Abelian solutions and discuss their interpretation. We prove a no-go theorem ruling out the existence of soliton solutions. Thus the semi-classical approximation shows no baryons in the case of massless quarks, a result derived before in the strong-coupling limit only. 1

In pure N = 1 supersymmetric Yang-Mills with gauge group SU(N), the domain walls which separate t... more In pure N = 1 supersymmetric Yang-Mills with gauge group SU(N), the domain walls which separate the N vacua have been argued, on the basis of string theory realizations, to be D-branes for the confining string. In a certain limit, this means that a configuration of k parallel domain walls is described by a 2 + 1dimensional U(k) gauge theory. This theory has been identified by Acharya and Vafa as the U(k) gauge theory with 4 supercharges broken by a Chern-Simons term of level N in such a way that 2 supercharges are preserved. We argue further that the gauge coupling of the domain wall gauge theory goes like g 2 ∼ Λ/N, for large N. In the case of two domain walls, we show that the U(2) world-volume theory generates a quadratic potential on the Coulomb branch at two loops in perturbation theory which is consistent with there being a supersymmetric bound state of the two wall system. A mass gap of order Λ/N is generated around the supersymmetric minimum and we estimate the size of the bound-state to be order Λ/ √ N . At large distance the potential reaches a constant that can qualitatively account for the binding energy of the two walls even though stringy effects are not, strictly speaking, decoupled.