We construct solutions of type IIB supergravity corresponding to 7 branes, an O7 plane and 3 bran... more We construct solutions of type IIB supergravity corresponding to 7 branes, an O7 plane and 3 branes. By considering a probe moving in this background, with constant coupling and an AdS 5 component in its geometry, we are able to reproduce the exact low energy effective action for N = 2 super Yang-Mills theory with gauge group SU (2) and N f = 4 massless flavors. After turning on a mass for the flavors we find corrections to the AdS 5 geometry. In addition, the coupling shows a power law dependence on the energy scale of the theory. The origin of the power law behaviour of the coupling is traced back to instanton corrections. Instanton corrections to the four derivative terms in the low energy effective action are correctly obtained from a probe analysis. We study how these instanton corrections are reflected in the background geometry by calculating the quark-antiquark potential. Finally we consider a solution corresponding to an asymptotically free field theory. Again, the leading form of the four derivative terms in the low energy effective action are in complete agreement with field theory expectations.
Following the recent work of hep-th/0405076 we discuss the emergence of D-brane instanton solutio... more Following the recent work of hep-th/0405076 we discuss the emergence of D-brane instanton solutions in c=0 noncritical string theory. Our emphasis is on finding the D-instanton effects in a field theoretic setting. Using the framework of single matrix collective field theory (CSFT) we exhibit the appearance of such solutions. Some subtle issues regarding the form of the field theory equations, the comparison with string equations and the importance of a finite N exclusion principle are also discussed.
The g Y M perturbed, non supersymmetric extension of the dual single matrix description of 1/2 BP... more The g Y M perturbed, non supersymmetric extension of the dual single matrix description of 1/2 BPS states, within the Hilbert space reduction to the oscillator subsector associated with chiral primaries is considered. This matrix model is described in terms of a single hermitean matrix. It is found that, apart from a trivial shift in the energy, the large N background, spectrum and interaction of invariant states are independent of g Y M. This property applies to more general D terms.
We continue the development of a systematic procedure for deriving closed string pp wave string f... more We continue the development of a systematic procedure for deriving closed string pp wave string field theory from the large N Berenstein-Maldacena-Nastase limit. In the present paper the effects of the Yang-Mills interaction are considered in detail for general BMN states. The SFT interaction with the appropriate operator insertion at the interaction point is demonstrated.
We study the correspondence between the linear matrix model and the interacting nonlinear string ... more We study the correspondence between the linear matrix model and the interacting nonlinear string theory. Starting from the simple matrix harmonic oscillator states, we derive in a direct way scattering amplitudes of 2-dimensional strings, exhibiting the nonlinear equation generating arbitrary N-point tree amplitudes. An even closer connection between the matrix model and the conformal string theory is seen in studies of the symmetry algebra of the system.
We generalize the collective field theory to include supersymmetry. This provides a field theory ... more We generalize the collective field theory to include supersymmetry. This provides a field theory of supersymmetric non-critical strings. We demonstrate supersymmetry at the operator level. In studying small fluctuations a massless Majorana fermion is found as a partner to the tachyon.
In the context of the AdS 4 /CF T 3 correspondence between higher spin fields and vector theories... more In the context of the AdS 4 /CF T 3 correspondence between higher spin fields and vector theories, we use the constructive bilocal fields based approach to this correspondence, to demonstrate, at the IR critical point of the interacting vector theory and directly in the bulk, the removal of the ∆ = 1 (s = 0) state from the higher spins field spectrum, and to exhibit simple Klein-Gordon higher spin Hamiltonians. The bulk variables and higher spin fields are obtained in a simple manner from boundary bilocals, by the change of variables previously derived for the U V critical point (in momentum space), together with a field redefinition.
We discuss the canonical structure of the collective formulation of Vector Model/Higher Spin Dual... more We discuss the canonical structure of the collective formulation of Vector Model/Higher Spin Duality in AdS_4. This involves a construction of bulk AdS Higher Spin fields through a time-like bi-local Map, with a Hamiltonian and canonical structure which are established to all orders in 1/N.
We pursue the construction of higher-spin theory in AdS_4 from CFT_3 of the O(N) vector model in ... more We pursue the construction of higher-spin theory in AdS_4 from CFT_3 of the O(N) vector model in terms of canonical collective fields. In null plane quantization an exact map is established between the two spaces. The coordinates of the AdS_4 space-time are generated from the collective coordinates of the bi-local field. This, in the light cone gauge, provides an exact one to one reconstruction of bulk AdS_4 space-time and higher-spin fields.
We consider Gaussian ensembles of m N x N complex matrices. We identify an enhanced symmetry in t... more We consider Gaussian ensembles of m N x N complex matrices. We identify an enhanced symmetry in the system and the resultant closed subsector, which is naturally associated with the radial sector of the theory. The density of radial eigenvalues is obtained in the large N limit. It is of the Wigner form only for m=1. For m \ge 2, the new form of the density is obtained.
The large N dynamics of a subsector of d=0 interacting complex multi matrix systems, which is nat... more The large N dynamics of a subsector of d=0 interacting complex multi matrix systems, which is naturally parametrized by a matrix valued radial coordinate, and which embodies the canonical AdS/CFT relationship between 't Hooft's coupling constant and radius, is obtained. Unlike the case of the single complex matrix, for two or more complex matrices a new repulsive logarithmic potential is present, as a result of which the density of radial eigenvalues has support on an hyper annulus. For the single complex matrix, the integral over the angular degrees of freedom of the Yang-Mills interaction can be carried out exactly, and in the presence of an harmonic potential, the density of radial eigenvalues is shown to be of the Wigner type.
Employing the world line spinning particle picture. We discuss the appearance of several differen... more Employing the world line spinning particle picture. We discuss the appearance of several different 'gauges' which we use to gain a deeper explanation of the Collective/Gravity identification. We discuss transformations and algebraic equivalences between them. For a bulk identification we develop a 'gauge independent' representation where all gauge constraints are eliminated. This 'gauge reduction' of Higher Spin Gravity demonstrates that the physical content of 4D AdS HS theory is represented by the dynamics of an unconstrained scalar field in 6d. It is in this gauge reduced form that HS Theory can be seen to be equivalent to a 3 + 3 dimensional bi-local collective representation of CFT 3 .
Journal of Physics A: Mathematical and Theoretical, 2015
We discuss the canonical structure of the collective formulation of Vector Model/Higher Spin Dual... more We discuss the canonical structure of the collective formulation of Vector Model/Higher Spin Duality in AdS 4 . This involves a construction of bulk AdS Higher Spin fields through a time-like bi-local Map, with a Hamiltonian and canonical structure which are established to all orders in 1/N .
We pursue the construction of higher-spin theory in AdS4 from CFT3 of the O(N) vector model in te... more We pursue the construction of higher-spin theory in AdS4 from CFT3 of the O(N) vector model in terms of canonical collective fields. In null-plane quantization an exact map is established between the two spaces. The coordinates of the AdS4 space-time are generated from the collective coordinates of the bi-local field. This, in the light-cone gauge, provides an exact one-to-one reconstruction of bulk AdS4 space-time and higher-spin fields.
Following the work of Maldacena and Zhiboedov, we study the implementation of the Coleman-Mandula... more Following the work of Maldacena and Zhiboedov, we study the implementation of the Coleman-Mandula theorem in the free O(N)/Higher Spin correspondence. In the bi-local framework we first define an S-matrix for scattering of collective dipoles. Its evaluation in the case of free UV fixed point theory leads to the result S=1 stated in the title. We also present an appropriate field transformation that is seen to transform away all the non-linear 1/N interactions of this theory. A change of boundary conditions and/or external potentials results in a nontrivial S-matrix.
The supersymmetric collective field theory with the potential v ′ (x) = ωx − η x is studied, moti... more The supersymmetric collective field theory with the potential v ′ (x) = ωx − η x is studied, motivated by the matrix model proposed by Jevicki and Yoneya to describe two dimensional string theory in a black hole background. Consistency with supersymmetry enforces a two band solution. A supersymmetric classical configuration is found, and interpreted in terms of the density of zeros of certain Laguerre polynomials. The spectrum of the model is then studied and is seen to correspond to a massless scalar and a majorana fermion. The x space eigenfunctions are constructed and expressed in terms of Chebyshev polynomials. Higher order interactions are also discussed.
We consider the computation of out-of-time-ordered correlators (OTOCs) in the fishnet theories, w... more We consider the computation of out-of-time-ordered correlators (OTOCs) in the fishnet theories, with a mass term added. These fields theories are not unitary. We compute the growth exponent, in the planar limit, at any value of the coupling and show that the model exhibits chaos. At strong coupling the growth exponent violates the Maldacena-Shenker-Stanford bound. We also consider the mass deformed versions of the six dimensional honeycomb theories, which can also be solved in the planar limit. The honeycomb theory shows a very similar behavior to that exhibited by the fishnet theory.
In this work we revisit the problem of solving multi-matrix systems through numerical large N met... more In this work we revisit the problem of solving multi-matrix systems through numerical large N methods. The framework is a collective, loop space representation which provides a constrained optimization problem, addressed through master-field minimization. This scheme applies both to multi-matrix integrals (c = 0 systems) and multi-matrix quantum mechanics (c = 1). The complete fluctuation spectrum is also computable in the above scheme, and is of immediate physical relevance in the later case. The complexity (and the growth of degrees of freedom) at large N have stymied earlier attempts and in the present work we present significant improvements in this regard. The (constrained) minimization and spectrum calculations are easily achieved with close to 10 variables, giving solution to Migdal-Makeenko, and collective field equations. Considering the large number of dynamical (loop) variables and the extreme nonlinearity of the problem, high precision is obtained when confronted with so...
The large N dynamics of a subsector of d = 0 interacting complex multi matrix systems, which is n... more The large N dynamics of a subsector of d = 0 interacting complex multi matrix systems, which is naturally parametrized by a matrix valued radial coordinate, and which embodies the canonical AdS/CFT relationship between 't Hooft's coupling constant and radius, is obtained. Unlike the case of the single complex matrix, for two or more complex matrices a new repulsive logarithmic potential is present, as a result of which the density of radial eigenvalues has suport on an hyper annulus. For the single complex matrix, the integral over the angular degrees of freedom can be carried out exactly, and in the presence of an harmonic potential, the density of radial eigenvalues is shown to be of the Wigner type.
We consider the quantum mechanics of an even number of space indexed hermitian matrices. Upon com... more We consider the quantum mechanics of an even number of space indexed hermitian matrices. Upon complexification, we show that a closed subsector naturally parametrized by a matrix valued radial coordinate has a description in terms of non interacting s-state “radial fermions” with an emergent De Alfaro, Fubini and Furlan type potential, present only for two or more complex matrices. The concomitant AdS 2 symmetry is identified.The large N description in terms of the density of radial eigenvalues is also described.
We construct solutions of type IIB supergravity corresponding to 7 branes, an O7 plane and 3 bran... more We construct solutions of type IIB supergravity corresponding to 7 branes, an O7 plane and 3 branes. By considering a probe moving in this background, with constant coupling and an AdS 5 component in its geometry, we are able to reproduce the exact low energy effective action for N = 2 super Yang-Mills theory with gauge group SU (2) and N f = 4 massless flavors. After turning on a mass for the flavors we find corrections to the AdS 5 geometry. In addition, the coupling shows a power law dependence on the energy scale of the theory. The origin of the power law behaviour of the coupling is traced back to instanton corrections. Instanton corrections to the four derivative terms in the low energy effective action are correctly obtained from a probe analysis. We study how these instanton corrections are reflected in the background geometry by calculating the quark-antiquark potential. Finally we consider a solution corresponding to an asymptotically free field theory. Again, the leading form of the four derivative terms in the low energy effective action are in complete agreement with field theory expectations.
Following the recent work of hep-th/0405076 we discuss the emergence of D-brane instanton solutio... more Following the recent work of hep-th/0405076 we discuss the emergence of D-brane instanton solutions in c=0 noncritical string theory. Our emphasis is on finding the D-instanton effects in a field theoretic setting. Using the framework of single matrix collective field theory (CSFT) we exhibit the appearance of such solutions. Some subtle issues regarding the form of the field theory equations, the comparison with string equations and the importance of a finite N exclusion principle are also discussed.
The g Y M perturbed, non supersymmetric extension of the dual single matrix description of 1/2 BP... more The g Y M perturbed, non supersymmetric extension of the dual single matrix description of 1/2 BPS states, within the Hilbert space reduction to the oscillator subsector associated with chiral primaries is considered. This matrix model is described in terms of a single hermitean matrix. It is found that, apart from a trivial shift in the energy, the large N background, spectrum and interaction of invariant states are independent of g Y M. This property applies to more general D terms.
We continue the development of a systematic procedure for deriving closed string pp wave string f... more We continue the development of a systematic procedure for deriving closed string pp wave string field theory from the large N Berenstein-Maldacena-Nastase limit. In the present paper the effects of the Yang-Mills interaction are considered in detail for general BMN states. The SFT interaction with the appropriate operator insertion at the interaction point is demonstrated.
We study the correspondence between the linear matrix model and the interacting nonlinear string ... more We study the correspondence between the linear matrix model and the interacting nonlinear string theory. Starting from the simple matrix harmonic oscillator states, we derive in a direct way scattering amplitudes of 2-dimensional strings, exhibiting the nonlinear equation generating arbitrary N-point tree amplitudes. An even closer connection between the matrix model and the conformal string theory is seen in studies of the symmetry algebra of the system.
We generalize the collective field theory to include supersymmetry. This provides a field theory ... more We generalize the collective field theory to include supersymmetry. This provides a field theory of supersymmetric non-critical strings. We demonstrate supersymmetry at the operator level. In studying small fluctuations a massless Majorana fermion is found as a partner to the tachyon.
In the context of the AdS 4 /CF T 3 correspondence between higher spin fields and vector theories... more In the context of the AdS 4 /CF T 3 correspondence between higher spin fields and vector theories, we use the constructive bilocal fields based approach to this correspondence, to demonstrate, at the IR critical point of the interacting vector theory and directly in the bulk, the removal of the ∆ = 1 (s = 0) state from the higher spins field spectrum, and to exhibit simple Klein-Gordon higher spin Hamiltonians. The bulk variables and higher spin fields are obtained in a simple manner from boundary bilocals, by the change of variables previously derived for the U V critical point (in momentum space), together with a field redefinition.
We discuss the canonical structure of the collective formulation of Vector Model/Higher Spin Dual... more We discuss the canonical structure of the collective formulation of Vector Model/Higher Spin Duality in AdS_4. This involves a construction of bulk AdS Higher Spin fields through a time-like bi-local Map, with a Hamiltonian and canonical structure which are established to all orders in 1/N.
We pursue the construction of higher-spin theory in AdS_4 from CFT_3 of the O(N) vector model in ... more We pursue the construction of higher-spin theory in AdS_4 from CFT_3 of the O(N) vector model in terms of canonical collective fields. In null plane quantization an exact map is established between the two spaces. The coordinates of the AdS_4 space-time are generated from the collective coordinates of the bi-local field. This, in the light cone gauge, provides an exact one to one reconstruction of bulk AdS_4 space-time and higher-spin fields.
We consider Gaussian ensembles of m N x N complex matrices. We identify an enhanced symmetry in t... more We consider Gaussian ensembles of m N x N complex matrices. We identify an enhanced symmetry in the system and the resultant closed subsector, which is naturally associated with the radial sector of the theory. The density of radial eigenvalues is obtained in the large N limit. It is of the Wigner form only for m=1. For m \ge 2, the new form of the density is obtained.
The large N dynamics of a subsector of d=0 interacting complex multi matrix systems, which is nat... more The large N dynamics of a subsector of d=0 interacting complex multi matrix systems, which is naturally parametrized by a matrix valued radial coordinate, and which embodies the canonical AdS/CFT relationship between 't Hooft's coupling constant and radius, is obtained. Unlike the case of the single complex matrix, for two or more complex matrices a new repulsive logarithmic potential is present, as a result of which the density of radial eigenvalues has support on an hyper annulus. For the single complex matrix, the integral over the angular degrees of freedom of the Yang-Mills interaction can be carried out exactly, and in the presence of an harmonic potential, the density of radial eigenvalues is shown to be of the Wigner type.
Employing the world line spinning particle picture. We discuss the appearance of several differen... more Employing the world line spinning particle picture. We discuss the appearance of several different 'gauges' which we use to gain a deeper explanation of the Collective/Gravity identification. We discuss transformations and algebraic equivalences between them. For a bulk identification we develop a 'gauge independent' representation where all gauge constraints are eliminated. This 'gauge reduction' of Higher Spin Gravity demonstrates that the physical content of 4D AdS HS theory is represented by the dynamics of an unconstrained scalar field in 6d. It is in this gauge reduced form that HS Theory can be seen to be equivalent to a 3 + 3 dimensional bi-local collective representation of CFT 3 .
Journal of Physics A: Mathematical and Theoretical, 2015
We discuss the canonical structure of the collective formulation of Vector Model/Higher Spin Dual... more We discuss the canonical structure of the collective formulation of Vector Model/Higher Spin Duality in AdS 4 . This involves a construction of bulk AdS Higher Spin fields through a time-like bi-local Map, with a Hamiltonian and canonical structure which are established to all orders in 1/N .
We pursue the construction of higher-spin theory in AdS4 from CFT3 of the O(N) vector model in te... more We pursue the construction of higher-spin theory in AdS4 from CFT3 of the O(N) vector model in terms of canonical collective fields. In null-plane quantization an exact map is established between the two spaces. The coordinates of the AdS4 space-time are generated from the collective coordinates of the bi-local field. This, in the light-cone gauge, provides an exact one-to-one reconstruction of bulk AdS4 space-time and higher-spin fields.
Following the work of Maldacena and Zhiboedov, we study the implementation of the Coleman-Mandula... more Following the work of Maldacena and Zhiboedov, we study the implementation of the Coleman-Mandula theorem in the free O(N)/Higher Spin correspondence. In the bi-local framework we first define an S-matrix for scattering of collective dipoles. Its evaluation in the case of free UV fixed point theory leads to the result S=1 stated in the title. We also present an appropriate field transformation that is seen to transform away all the non-linear 1/N interactions of this theory. A change of boundary conditions and/or external potentials results in a nontrivial S-matrix.
The supersymmetric collective field theory with the potential v ′ (x) = ωx − η x is studied, moti... more The supersymmetric collective field theory with the potential v ′ (x) = ωx − η x is studied, motivated by the matrix model proposed by Jevicki and Yoneya to describe two dimensional string theory in a black hole background. Consistency with supersymmetry enforces a two band solution. A supersymmetric classical configuration is found, and interpreted in terms of the density of zeros of certain Laguerre polynomials. The spectrum of the model is then studied and is seen to correspond to a massless scalar and a majorana fermion. The x space eigenfunctions are constructed and expressed in terms of Chebyshev polynomials. Higher order interactions are also discussed.
We consider the computation of out-of-time-ordered correlators (OTOCs) in the fishnet theories, w... more We consider the computation of out-of-time-ordered correlators (OTOCs) in the fishnet theories, with a mass term added. These fields theories are not unitary. We compute the growth exponent, in the planar limit, at any value of the coupling and show that the model exhibits chaos. At strong coupling the growth exponent violates the Maldacena-Shenker-Stanford bound. We also consider the mass deformed versions of the six dimensional honeycomb theories, which can also be solved in the planar limit. The honeycomb theory shows a very similar behavior to that exhibited by the fishnet theory.
In this work we revisit the problem of solving multi-matrix systems through numerical large N met... more In this work we revisit the problem of solving multi-matrix systems through numerical large N methods. The framework is a collective, loop space representation which provides a constrained optimization problem, addressed through master-field minimization. This scheme applies both to multi-matrix integrals (c = 0 systems) and multi-matrix quantum mechanics (c = 1). The complete fluctuation spectrum is also computable in the above scheme, and is of immediate physical relevance in the later case. The complexity (and the growth of degrees of freedom) at large N have stymied earlier attempts and in the present work we present significant improvements in this regard. The (constrained) minimization and spectrum calculations are easily achieved with close to 10 variables, giving solution to Migdal-Makeenko, and collective field equations. Considering the large number of dynamical (loop) variables and the extreme nonlinearity of the problem, high precision is obtained when confronted with so...
The large N dynamics of a subsector of d = 0 interacting complex multi matrix systems, which is n... more The large N dynamics of a subsector of d = 0 interacting complex multi matrix systems, which is naturally parametrized by a matrix valued radial coordinate, and which embodies the canonical AdS/CFT relationship between 't Hooft's coupling constant and radius, is obtained. Unlike the case of the single complex matrix, for two or more complex matrices a new repulsive logarithmic potential is present, as a result of which the density of radial eigenvalues has suport on an hyper annulus. For the single complex matrix, the integral over the angular degrees of freedom can be carried out exactly, and in the presence of an harmonic potential, the density of radial eigenvalues is shown to be of the Wigner type.
We consider the quantum mechanics of an even number of space indexed hermitian matrices. Upon com... more We consider the quantum mechanics of an even number of space indexed hermitian matrices. Upon complexification, we show that a closed subsector naturally parametrized by a matrix valued radial coordinate has a description in terms of non interacting s-state “radial fermions” with an emergent De Alfaro, Fubini and Furlan type potential, present only for two or more complex matrices. The concomitant AdS 2 symmetry is identified.The large N description in terms of the density of radial eigenvalues is also described.
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Papers by João Rodrigues