David Berenstein - Academia.edu (original) (raw)
Papers by David Berenstein
Physics Letters B, 2001
We discuss aspects of the algebraic geometry of compact non-commutative Calabi-Yau manifolds. In ... more We discuss aspects of the algebraic geometry of compact non-commutative Calabi-Yau manifolds. In this setting, it is appropriate to consider local holomorphic algebras which can be glued together into a compact Calabi-Yau algebra. We consider two examples: a toroidal orbifold T 6 /Z 2 ×Z 2 , and an orbifold of the quintic in CP 4 , each with discrete torsion. The non-commutative geometry tools are enough to describe various properties of the orbifolds. First, one describes correctly the fractionation of branes at singularities. Secondly, for the first example we show that one can recover explicitly a large slice of the moduli space of complex structures which deform the orbifold. For this example we also show that we get the correct counting of complex structure deformations at the orbifold point by using traces of non-commutative differential forms (cyclic homology).
Physical Review D
In this paper we study a quench protocol on thermofield double states in the presence of time-rev... more In this paper we study a quench protocol on thermofield double states in the presence of time-reversal symmetry that is inspired by the work of Gao, Jafferis and Wall. The deformation is a product of hermitian operators on the left and right systems that are identical to each other and that lasts for a small amount of time. We study the linear dependence on the quench to the properties of the deformation under time reversal. If the quench is time symmetric, then the linear response after the quench of all T-even operators vanishes. This includes the response of the energy on the left system and all the thermodynamic expectation values (the time averaged expectation values of the operators). Also, we show under an assumption of nondegeneracy of the Hamiltonian that the entanglement entropy between left and right is not affected to this order. We also study a variation of the quench where an instantaneous deformation is given by an operator of fixed T-parity and it's time derivative. It is shown that the sign of the response of the Hamiltonian is correlated with the T-parity of the operator. We can then choose the sign of the amplitude of the quench to result in a reduction in the energy. This implies a reduction of the entanglement entropy between both sides.
International Journal of Modern Physics A
We study various corrections of correlation functions to leading order in conformal perturbation ... more We study various corrections of correlation functions to leading order in conformal perturbation theory, both on the cylinder and on the plane. Many problems on the cylinder are mathematically equivalent to those in the plane if we give the perturbations a position dependent scaling profile. The integrals to be done are then similar to those in the study of correlation functions with one additional insertion at the center of the profile. We will be primarily interested in the divergence structure of these corrections when computed in dimensional regularization. In particular, we show that the logarithmic divergences (enhancements) that show up in the plane under these circumstances can be understood in terms of resonant behavior in time dependent perturbation theory, for a transition between states that is induced by an oscillatory perturbation on the cylinder.
Journal of High Energy Physics
The gravity side of the gauge/gravity duality predicts the existence of small black holes with ne... more The gravity side of the gauge/gravity duality predicts the existence of small black holes with negative specific heat. A free theory of strings has a Hagedorn behavior, but it does not lead to negative specific heat. To understand such states one needs to consider a theory of interacting strings. In the dual gauge theory, the string interactions are related to non-planar diagrams. In this paper the simplest gauged matrix model of two free matrices, that has Hagedorn behavior is analyzed in detail. A simple double trace deformation of the Hamiltonian, proportional to the square of the free Hamiltonian is studied. If the interaction has a negative sign, mimicking a gravitational attraction, one produces states with negative specific heat perturbatively and one can still compute the equation of state relating the entropy and the energy. A more general argument based on non-planar interactions that are random and that grow faster in strength than the planar diagrams as a function of the...
Classical and Quantum Gravity
We consider effective field theory around classical background geometries with a gauge theory dua... more We consider effective field theory around classical background geometries with a gauge theory dual, in the class of LLM geometries. These are dual to half-BPS states of N = 4 SYM. We find that the language of code subspaces is natural for discussing the set of nearby states, which are built by acting with effective fields on these backgrounds. This work extends our previous work by going beyond the strict infinite N limit. We further discuss how one can extract the topology of the state beyond N → ∞ and find that uncertainty and entanglement entropy calculations still provide a useful tool to do so. Finally, we discuss obstructions to writing down a globally defined metric operator. We find that the answer depends on the choice of reference state that one starts with. Therefore there is ambiguity in trying to write an operator that describes the metric globally.
Journal of High Energy Physics
We consider the gauged free fermionic matrix model, for a single fermionic matrix. In the large N... more We consider the gauged free fermionic matrix model, for a single fermionic matrix. In the large N limit this system describes a c = 1/2 chiral fermion in 1 + 1 dimensions. The Gauss’ law constraint implies that to obtain a physical state, indices of the fermionic matrices must be fully contracted, to form a singlet. There are two ways in which this can be achieved: one can consider a trace basis formed from products of traces of fermionic matrices or one can consider a Schur function basis, labeled by Young diagrams. The Schur polynomials for the fermions involve a twisted character, as a consequence of Fermi statistics. The main result of this paper is a proof that the trace and Schur bases coincide up to a simple normalization coefficient that we have computed.
Journal of High Energy Physics
Large N gauged multi-matrix quantum mechanical models usually have a first order Hagedorn transit... more Large N gauged multi-matrix quantum mechanical models usually have a first order Hagedorn transition, related to deconfinement. In this transition the change of the energy and entropy is of order N 2 at the critical temperature. This paper studies the microcanonical ensemble of the model at intermediate energies 1 ≪ E ≪ N 2 in the coexistence region for the first order phase transition. Evidence is provided for a partial deconfinement phase where submatrix degrees of freedom for a U(M) subgroup of U(N), with M ≪ N have an excitation energy of order M 2 and are effectively phase separated from the other degrees of freedom. These results also provide a simple example of the Susskind-Horowitz-Polchinski correspondence principle where a transition from a long string to a black hole is smooth. Implications for the dual configurations of small black holes in AdS are discussed.
Journal of High Energy Physics
Black holes have an enormous underlying space of microstates, but universal macroscopic physics c... more Black holes have an enormous underlying space of microstates, but universal macroscopic physics characterized by mass, charge and angular momentum as well as a causally disconnected interior. This leads to two related puzzles: (1) How does the effective factorization of interior and exterior degrees of freedom emerge in gravity?, and (2) How does the underlying degeneracy of states wind up having a geometric realization in the horizon area and in properties of the singularity? We explore these puzzles in the context of an incipient black hole in the AdS/CFT correspondence, the microstates of which are dual to half-BPS states of the mathcalN\mathcal{N}mathcalN N = 4 super-Yang-Mills theory. First, we construct a code subspace for this black hole and show how to organize it as a tensor product of a universal macroscopic piece (describing the exterior), and a factor corresponding to the microscopic degrees of freedom (describing the interior). We then study the classical phase space and symplect...
Journal of High Energy Physics
We show that superpositions of classical states in quantum gravity with fixed topology can lead t... more We show that superpositions of classical states in quantum gravity with fixed topology can lead to new classical states with a different topology. We study this phenomenon in a particular limit of the LLM geometries. In this limit, the UV complete minisuperspace of allowed quantum states is exactly given by the Hilbert space of a free chiral boson in two dimensions. We construct this chiral boson purely in terms of combinatorial objects associated with the permutation group. As a byproduct of this analysis, we rederive the Murnaghan-Nakayama rule for characters of the permutation group. We are able to express this rule in terms of operator relations for raising and lowering operators on the Hilbert space of states in a free fermion basis. Our construction provides a preferred notion of bulk locality by studying an appropriate notion of D-brane state generating functions. We describe how multi-droplet LLM geometries with different topologies give new classical limits of the free chiral boson, even though they can be written as superpositions of coherent states with trivial topology. As a consequence, topology cannot be accessed by a single operator measurement in this quantum system. We study other non-linear measurements in the quantum wave-function, based on uncertainty and entanglement between modes of the chiral boson, that can be used as order parameters to measure the topology of such states.
Physical Review D
We study the smallest non-trivial matrix model that can be considered to be a (toy) model of a bl... more We study the smallest non-trivial matrix model that can be considered to be a (toy) model of a black hole. The model consists of a pair of 2 × 2 traceless hermitian matrices with a commutator squared potential and an SU (2) gauge symmetry, plus an SO(2) rotation symmetry. We show that using the symmetries of the system, all but two of the variables can be separated. The two variables that remain display chaos and a transition from chaos to integrability when a parameter related to an SO(2) angular momentum is tuned to a critical value. We compute the Lyapunov exponents near this transition and study the critical exponent of the Lyapunov exponents near the critical point. We compare this transition to extremal rotating black holes.
International Journal of Modern Physics D
In this paper, we argue that for classical configurations of gravity in the AdS/CFT setup, it is ... more In this paper, we argue that for classical configurations of gravity in the AdS/CFT setup, it is in general impossible to reconstruct the bulk geometry from the leading asymptotic behavior of the classical fields in gravity alone. This is possible sufficiently near the vacuum, but not more generally. We argue this by using a counter-example that utilizes the supersymmetric geometries constructed by Lin, Lunin, and Maldacena. In the dual quantum field theory, the additional data required to complete the geometry is encoded in modes that near the vacuum geometry lie beyond the Planck scale.
Fortschritte der Physik
In this paper three notions of emergent geometry arising from the study of gauge/gravity duals ar... more In this paper three notions of emergent geometry arising from the study of gauge/gravity duals are discussed. The unifying theme behind these notions of emergent geometry is that one can derive properties of the effective action of a probe or excitation around some configuration in gauge theory which can be argued to be localized at a particular position in the gravity dual, and match this description to various degrees of accuracy in the gravity dual. The three examples discussed are giant gravitons in AdS 5 × S 5 , open strings stretching between these giants and the probe dynamics of a D0 brane in the presence of a thermal matrix configuration of the BFSS matrix model.
Physical Review Letters
In the context of LLM geometries, we show that superpositions of classical coherent states of tri... more In the context of LLM geometries, we show that superpositions of classical coherent states of trivial topology can give rise to new classical limits where the topology of spacetime has changed. We argue that this phenomenon implies that neither the topology nor the geometry of spacetime can be the result of an operator measurement. We address how to reconcile these statements with the usual semiclassical analysis of low energy effective field theory for gravity.
Physics Letters Section B, 2009
We provide a characterization of the set of configurations in N = 4 SYM theory that are dual to s... more We provide a characterization of the set of configurations in N = 4 SYM theory that are dual to small AdS black holes. Our construction shows that the black hole dual states are approximately thermal on a SU(M) subset of degrees of freedom of a SU(N) gauge theory. M is determined dynamically and the black hole degrees of freedom are dynamically insulated from the rest. These states are localized on the S 5 and have dynamical processes that correspond to matter absorption that make them behave as black objects.
In this paper it is argued that the central charge extension of the Coulomb branch of N = 4 SYM t... more In this paper it is argued that the central charge extension of the Coulomb branch of N = 4 SYM theory appears as a limit of Beisert's central charge extension of the planar N = 4 spin chain in the presence of boundaries. These boundaries are interpreted as D-branes that source the central charge and are realized as giant gravitons and dual giant gravitons in the AdS dual. The BPS states that correspond to short representations of the centrally extended algebra on the spin chain can stop from existing when they cross walls of stability that depend on the position of the branes. These walls can be understood easily at weak coupling in the SU(2) sector.
Eprint Arxiv Hep Th 0603103, Mar 1, 2006
This paper studies the compatibility of having a grand unification scheme for particle physics, w... more This paper studies the compatibility of having a grand unification scheme for particle physics, while at the same time having a perturbative string theory description of such a scheme on a Dbrane. This is studied in a model independent approach and finds a negative result. Some additional observations related to model building on branes are made.
We study a one parameter family of supersymmetric marginal deformations of N = 4 SYM with U(1) 3 ... more We study a one parameter family of supersymmetric marginal deformations of N = 4 SYM with U(1) 3 symmetry, known as β-deformations, to understand their dual AdS × X geometry, where X is a large classical geometry in the g 2 YM N → ∞ limit. We argue that we can determine whether or not X is geometric by studying the spectrum of open strings between giant gravitons states, as represented by operators in the field theory, as we take N → ∞ in certain double scaling limits. We study the conditions under which these open strings can give rise to a large number of states with energy far below the string scale. The number-theoretic properties of β are very important. When exp(iβ) is a root of unity, the space X is an orbifold. When exp(iβ) close to a root of unity in a double scaling limit sense, X corresponds to a finite deformation of the orbifold. Finally, if β is irrational, sporadic light states can be present.
Physical Review D Particles and Fields, Nov 13, 2008
ABSTRACT
Physics Letters B, 2001
We discuss aspects of the algebraic geometry of compact non-commutative Calabi-Yau manifolds. In ... more We discuss aspects of the algebraic geometry of compact non-commutative Calabi-Yau manifolds. In this setting, it is appropriate to consider local holomorphic algebras which can be glued together into a compact Calabi-Yau algebra. We consider two examples: a toroidal orbifold T 6 /Z 2 ×Z 2 , and an orbifold of the quintic in CP 4 , each with discrete torsion. The non-commutative geometry tools are enough to describe various properties of the orbifolds. First, one describes correctly the fractionation of branes at singularities. Secondly, for the first example we show that one can recover explicitly a large slice of the moduli space of complex structures which deform the orbifold. For this example we also show that we get the correct counting of complex structure deformations at the orbifold point by using traces of non-commutative differential forms (cyclic homology).
Physical Review D
In this paper we study a quench protocol on thermofield double states in the presence of time-rev... more In this paper we study a quench protocol on thermofield double states in the presence of time-reversal symmetry that is inspired by the work of Gao, Jafferis and Wall. The deformation is a product of hermitian operators on the left and right systems that are identical to each other and that lasts for a small amount of time. We study the linear dependence on the quench to the properties of the deformation under time reversal. If the quench is time symmetric, then the linear response after the quench of all T-even operators vanishes. This includes the response of the energy on the left system and all the thermodynamic expectation values (the time averaged expectation values of the operators). Also, we show under an assumption of nondegeneracy of the Hamiltonian that the entanglement entropy between left and right is not affected to this order. We also study a variation of the quench where an instantaneous deformation is given by an operator of fixed T-parity and it's time derivative. It is shown that the sign of the response of the Hamiltonian is correlated with the T-parity of the operator. We can then choose the sign of the amplitude of the quench to result in a reduction in the energy. This implies a reduction of the entanglement entropy between both sides.
International Journal of Modern Physics A
We study various corrections of correlation functions to leading order in conformal perturbation ... more We study various corrections of correlation functions to leading order in conformal perturbation theory, both on the cylinder and on the plane. Many problems on the cylinder are mathematically equivalent to those in the plane if we give the perturbations a position dependent scaling profile. The integrals to be done are then similar to those in the study of correlation functions with one additional insertion at the center of the profile. We will be primarily interested in the divergence structure of these corrections when computed in dimensional regularization. In particular, we show that the logarithmic divergences (enhancements) that show up in the plane under these circumstances can be understood in terms of resonant behavior in time dependent perturbation theory, for a transition between states that is induced by an oscillatory perturbation on the cylinder.
Journal of High Energy Physics
The gravity side of the gauge/gravity duality predicts the existence of small black holes with ne... more The gravity side of the gauge/gravity duality predicts the existence of small black holes with negative specific heat. A free theory of strings has a Hagedorn behavior, but it does not lead to negative specific heat. To understand such states one needs to consider a theory of interacting strings. In the dual gauge theory, the string interactions are related to non-planar diagrams. In this paper the simplest gauged matrix model of two free matrices, that has Hagedorn behavior is analyzed in detail. A simple double trace deformation of the Hamiltonian, proportional to the square of the free Hamiltonian is studied. If the interaction has a negative sign, mimicking a gravitational attraction, one produces states with negative specific heat perturbatively and one can still compute the equation of state relating the entropy and the energy. A more general argument based on non-planar interactions that are random and that grow faster in strength than the planar diagrams as a function of the...
Classical and Quantum Gravity
We consider effective field theory around classical background geometries with a gauge theory dua... more We consider effective field theory around classical background geometries with a gauge theory dual, in the class of LLM geometries. These are dual to half-BPS states of N = 4 SYM. We find that the language of code subspaces is natural for discussing the set of nearby states, which are built by acting with effective fields on these backgrounds. This work extends our previous work by going beyond the strict infinite N limit. We further discuss how one can extract the topology of the state beyond N → ∞ and find that uncertainty and entanglement entropy calculations still provide a useful tool to do so. Finally, we discuss obstructions to writing down a globally defined metric operator. We find that the answer depends on the choice of reference state that one starts with. Therefore there is ambiguity in trying to write an operator that describes the metric globally.
Journal of High Energy Physics
We consider the gauged free fermionic matrix model, for a single fermionic matrix. In the large N... more We consider the gauged free fermionic matrix model, for a single fermionic matrix. In the large N limit this system describes a c = 1/2 chiral fermion in 1 + 1 dimensions. The Gauss’ law constraint implies that to obtain a physical state, indices of the fermionic matrices must be fully contracted, to form a singlet. There are two ways in which this can be achieved: one can consider a trace basis formed from products of traces of fermionic matrices or one can consider a Schur function basis, labeled by Young diagrams. The Schur polynomials for the fermions involve a twisted character, as a consequence of Fermi statistics. The main result of this paper is a proof that the trace and Schur bases coincide up to a simple normalization coefficient that we have computed.
Journal of High Energy Physics
Large N gauged multi-matrix quantum mechanical models usually have a first order Hagedorn transit... more Large N gauged multi-matrix quantum mechanical models usually have a first order Hagedorn transition, related to deconfinement. In this transition the change of the energy and entropy is of order N 2 at the critical temperature. This paper studies the microcanonical ensemble of the model at intermediate energies 1 ≪ E ≪ N 2 in the coexistence region for the first order phase transition. Evidence is provided for a partial deconfinement phase where submatrix degrees of freedom for a U(M) subgroup of U(N), with M ≪ N have an excitation energy of order M 2 and are effectively phase separated from the other degrees of freedom. These results also provide a simple example of the Susskind-Horowitz-Polchinski correspondence principle where a transition from a long string to a black hole is smooth. Implications for the dual configurations of small black holes in AdS are discussed.
Journal of High Energy Physics
Black holes have an enormous underlying space of microstates, but universal macroscopic physics c... more Black holes have an enormous underlying space of microstates, but universal macroscopic physics characterized by mass, charge and angular momentum as well as a causally disconnected interior. This leads to two related puzzles: (1) How does the effective factorization of interior and exterior degrees of freedom emerge in gravity?, and (2) How does the underlying degeneracy of states wind up having a geometric realization in the horizon area and in properties of the singularity? We explore these puzzles in the context of an incipient black hole in the AdS/CFT correspondence, the microstates of which are dual to half-BPS states of the mathcalN\mathcal{N}mathcalN N = 4 super-Yang-Mills theory. First, we construct a code subspace for this black hole and show how to organize it as a tensor product of a universal macroscopic piece (describing the exterior), and a factor corresponding to the microscopic degrees of freedom (describing the interior). We then study the classical phase space and symplect...
Journal of High Energy Physics
We show that superpositions of classical states in quantum gravity with fixed topology can lead t... more We show that superpositions of classical states in quantum gravity with fixed topology can lead to new classical states with a different topology. We study this phenomenon in a particular limit of the LLM geometries. In this limit, the UV complete minisuperspace of allowed quantum states is exactly given by the Hilbert space of a free chiral boson in two dimensions. We construct this chiral boson purely in terms of combinatorial objects associated with the permutation group. As a byproduct of this analysis, we rederive the Murnaghan-Nakayama rule for characters of the permutation group. We are able to express this rule in terms of operator relations for raising and lowering operators on the Hilbert space of states in a free fermion basis. Our construction provides a preferred notion of bulk locality by studying an appropriate notion of D-brane state generating functions. We describe how multi-droplet LLM geometries with different topologies give new classical limits of the free chiral boson, even though they can be written as superpositions of coherent states with trivial topology. As a consequence, topology cannot be accessed by a single operator measurement in this quantum system. We study other non-linear measurements in the quantum wave-function, based on uncertainty and entanglement between modes of the chiral boson, that can be used as order parameters to measure the topology of such states.
Physical Review D
We study the smallest non-trivial matrix model that can be considered to be a (toy) model of a bl... more We study the smallest non-trivial matrix model that can be considered to be a (toy) model of a black hole. The model consists of a pair of 2 × 2 traceless hermitian matrices with a commutator squared potential and an SU (2) gauge symmetry, plus an SO(2) rotation symmetry. We show that using the symmetries of the system, all but two of the variables can be separated. The two variables that remain display chaos and a transition from chaos to integrability when a parameter related to an SO(2) angular momentum is tuned to a critical value. We compute the Lyapunov exponents near this transition and study the critical exponent of the Lyapunov exponents near the critical point. We compare this transition to extremal rotating black holes.
International Journal of Modern Physics D
In this paper, we argue that for classical configurations of gravity in the AdS/CFT setup, it is ... more In this paper, we argue that for classical configurations of gravity in the AdS/CFT setup, it is in general impossible to reconstruct the bulk geometry from the leading asymptotic behavior of the classical fields in gravity alone. This is possible sufficiently near the vacuum, but not more generally. We argue this by using a counter-example that utilizes the supersymmetric geometries constructed by Lin, Lunin, and Maldacena. In the dual quantum field theory, the additional data required to complete the geometry is encoded in modes that near the vacuum geometry lie beyond the Planck scale.
Fortschritte der Physik
In this paper three notions of emergent geometry arising from the study of gauge/gravity duals ar... more In this paper three notions of emergent geometry arising from the study of gauge/gravity duals are discussed. The unifying theme behind these notions of emergent geometry is that one can derive properties of the effective action of a probe or excitation around some configuration in gauge theory which can be argued to be localized at a particular position in the gravity dual, and match this description to various degrees of accuracy in the gravity dual. The three examples discussed are giant gravitons in AdS 5 × S 5 , open strings stretching between these giants and the probe dynamics of a D0 brane in the presence of a thermal matrix configuration of the BFSS matrix model.
Physical Review Letters
In the context of LLM geometries, we show that superpositions of classical coherent states of tri... more In the context of LLM geometries, we show that superpositions of classical coherent states of trivial topology can give rise to new classical limits where the topology of spacetime has changed. We argue that this phenomenon implies that neither the topology nor the geometry of spacetime can be the result of an operator measurement. We address how to reconcile these statements with the usual semiclassical analysis of low energy effective field theory for gravity.
Physics Letters Section B, 2009
We provide a characterization of the set of configurations in N = 4 SYM theory that are dual to s... more We provide a characterization of the set of configurations in N = 4 SYM theory that are dual to small AdS black holes. Our construction shows that the black hole dual states are approximately thermal on a SU(M) subset of degrees of freedom of a SU(N) gauge theory. M is determined dynamically and the black hole degrees of freedom are dynamically insulated from the rest. These states are localized on the S 5 and have dynamical processes that correspond to matter absorption that make them behave as black objects.
In this paper it is argued that the central charge extension of the Coulomb branch of N = 4 SYM t... more In this paper it is argued that the central charge extension of the Coulomb branch of N = 4 SYM theory appears as a limit of Beisert's central charge extension of the planar N = 4 spin chain in the presence of boundaries. These boundaries are interpreted as D-branes that source the central charge and are realized as giant gravitons and dual giant gravitons in the AdS dual. The BPS states that correspond to short representations of the centrally extended algebra on the spin chain can stop from existing when they cross walls of stability that depend on the position of the branes. These walls can be understood easily at weak coupling in the SU(2) sector.
Eprint Arxiv Hep Th 0603103, Mar 1, 2006
This paper studies the compatibility of having a grand unification scheme for particle physics, w... more This paper studies the compatibility of having a grand unification scheme for particle physics, while at the same time having a perturbative string theory description of such a scheme on a Dbrane. This is studied in a model independent approach and finds a negative result. Some additional observations related to model building on branes are made.
We study a one parameter family of supersymmetric marginal deformations of N = 4 SYM with U(1) 3 ... more We study a one parameter family of supersymmetric marginal deformations of N = 4 SYM with U(1) 3 symmetry, known as β-deformations, to understand their dual AdS × X geometry, where X is a large classical geometry in the g 2 YM N → ∞ limit. We argue that we can determine whether or not X is geometric by studying the spectrum of open strings between giant gravitons states, as represented by operators in the field theory, as we take N → ∞ in certain double scaling limits. We study the conditions under which these open strings can give rise to a large number of states with energy far below the string scale. The number-theoretic properties of β are very important. When exp(iβ) is a root of unity, the space X is an orbifold. When exp(iβ) close to a root of unity in a double scaling limit sense, X corresponds to a finite deformation of the orbifold. Finally, if β is irrational, sporadic light states can be present.
Physical Review D Particles and Fields, Nov 13, 2008
ABSTRACT