arXiv subjects

David Berenstein

Publications and source records attributed to David Berenstein.

At least 91 records · Page 5Linked to original sources

arXiv2010

The shape of emergent quantum geometry from an N=4 SYM minisuperspace approximation

We study numerically various wave functions in a gauged matrix quantum mechanics of six commuting hermitian $N\times N$ matrices. Our simulations span ranges of $N$ up to 10000. This system is a truncated and quenched version of N=4 SYM that serves as a minisuperspace approximation to the full ${\cal N}=4$ SYM system. This setup encodes aspects of the geometry of the AdS dual in terms of joint eigenvalue distributions for the matrices in the large $N$ limit. We analyze the problem of determining geometric measurements from these fluctuating distributions at finite $N$ and how fast they approach to the large N limit. We treat this eigenvalue geometry information as a proxy for geometric calculations in quantum gravity in a description where gravity is an emergent phenomenon. Our results show that care is needed in choosing the observables that measure the geometry: different choices of observables give different answers, have different size fluctuations at finite $N$ and they converge at different rates to the large $N$ limit. We find that some natural choices of observables are pathological at finite $N$ for $N$ sufficiently small. Finally, we note that the approach to the large $N$ limit does not seem to follow the expected convergence in powers of $1/N^2$ from planar diagram arguments. Our evidence suggests that different powers of $N$ appear, but convergence to large $N$ is rather slow so the values of $N$ we have explored might be too small to conclude this unambiguously.

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arXiv2010

The BPS spectrum of monopole operators in ABJM: towards a field theory description of the giant torus

We study the BPS spectrum of monopole operators in ABJM theory. First we work out the complete spectrum of the chiral ring by using a semiclassical analysis of the field theory compactified on a two sphere. By properly taking into account the full quantization condition of monopole charges, we show that the moduli space of ABJM theory with Chern-Simons level k, -k is a particular Z_k cover of the symmetric product of C^4/Z_k. We also work out in detail the spectrum of fluctuations around half-BPS monopole configurations and we find candidate states for a dual BPS configuration to the giant torus solution found by Nishioka and Takayanagi in the supergravity limit. We also discuss more general BPS states.

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arXiv2009

Aspects of ABJM orbifolds

We study abelian and non-abelian orbifolds of the ABJM model. We compute the precise moduli space of these models by analyzing the classical BPS equations for the theory on the cylinder, which include classical solutions of magnetic monopole operators. These determine the chiral ring of the theory, and thus they provide the complete set of order parameters determining the classical vacua of the theory. We show that the proper quantization of these semiclassical solutions gives us the topology of moduli space, including the additional quotient information due to the Chern-Simons levels. In general, we find that in the dual M-theory setup, the M-theory fiber is divided by the product of the Chern-Simons level times the order of the orbifold group, even in the non-abelian case. This depends non-trivially on how the different Chern-Simons terms have different levels in these constructions. We also see a direct relation in this setup between the Chern-Simons levels of the different groups and fluxes for fractional brane cycles. We also show that the problem of the moduli space can be much more easily analyzed by using the method of images and representation theory of crossed product algebras rather than dealing only with the quiver theory data.

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arXiv2008

Geometric aspects of dibaryon operators

The AdS/CFT correspondence for N=1 Super conformal field theories suggests that dibaryon operators are dual to D-brane states that are point like in AdS and that wrap various cycles in a Sasaki-Einstein manifold. It also suggests that the volume of the D-brane gives the R-charge of the corresponding operator. We elucidate various aspects of this correspondence, paying particular care to study the case of branes at the tip of three different Calabi Yau cones. We show that the arrows in the quiver diagram describing the conformal field theory can be thought of as global sections of a non-trivial holomorphic vector bundle over the Calabi-Yau geometry. We suggest that the zero locus of these sections gives the geometric map that lets us tie a particular dibaryon to a holomorphic cycle, by intersecting the corresponding cycle with the Sasaki-Einstein locus at fixed distance from the origin. We show that this can be compared with the corresponding volumes of the Sasaki-Einstein space and that one gets exact agreement between the volumes of the cycles identified with this procedure and the R-charges of the operators.

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arXiv2008

Small AdS black holes from SYM

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.

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arXiv2008

Three-dimensional N=6 SCFT's and their membrane dynamics

We analyze several aspects of the recent construction of three-dimensional conformal gauge theories by Aharony et al. in various regimes. We pay special attention to understanding how the M-theory geometry and interpretation can be extracted from the analysis of the field theory. We revisit the calculations of the moduli space of vacua and the complete characterization of chiral ring operators by analyzing the field theory compactified on a 2-sphere. We show that many of the states dual to these operators can be interpreted as D-brane states in the weak coupling limit. Also, various features of the dual AdS geometry can be obtained by performing a strong coupling expansion around moduli space configurations, even though one is not taking the planar expansion. In particular, we show that at strong coupling the corresponding weak coupling D-brane states of the chiral ring localize on particular submanifolds of the dual geometry that match the M-theory interpretation. We also study the massive spectrum of fields in the moduli space. We use this to investigate the dispersion relation of giant magnons from the field theory point of view. Our analysis predicts the exact functional form of the dispersion relation as a function of the world-sheet momentum, independently of integrability assumptions, but not the exact form with respect to the 't Hooft coupling. We also get the dispersion relation of bound states of giant magnons from first principles, providing evidence for the full integrability of the corresponding spin chain model at strong 't Hooft coupling.

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arXiv2008

Numerical tests of AdS/CFT at strong coupling

We study various correlation functions (two and three point functions) in a large $N$ matrix model of six commuting matrices with a numerical Monte Carlo algorithm. This is equivalent to a model of a gas of particles in six dimensions with a confining quadratic potential and logarithmic repulsions at finite temperature, where we are measuring the leading order non-gaussianities in the thermal fluctuations. This is a simplified model of the low energy dynamics of N=4 SYM at strong coupling. We find strong evidence that the simplified matrix model matches with the dual gravitational description of three point functions in the AdS/CFT correspondence.

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arXiv2008

A strong coupling expansion for N=4 SYM theory and other SCFT's

Recent progress towards understanding a strong coupling expansion for various superconformal field theories in four dimensions is described. First, the case of the maximally supersymmetric Yang Mills theory is analyzed, as well as many calculations that can be done directly at strong coupling and matched to the AdS dual geometry. Also, this understanding is extended to other AdS duals where the sphere is replaced by a Sasaki-Einstein manifold. Particular emphasis is made on matching exactly part of the supergravity dual spectrum of various of these field theories by using wave function methods.

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arXiv2008

Possible exotic stringy signatures at the LHC

In this paper I discuss some string inspired exotic colored matter particles that could be produced at the LHC, as well as the experimental signature for the observation of such states. Their most easily identifiable signature of this scenario is that many of these exotic particles would decay into standard model particles only via higher dimension operators in the effective field theory at a TeV scale. Some of these particles would only have three body decays into standard model particles.

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arXiv2007

Strings on conifolds from strong coupling dynamics, part I

A method to solve various aspects of the strong coupling expansion of the superconformal field theory duals of AdS_5 x X geometries from first principles is proposed. The main idea is that at strong coupling the configurations that dominate the low energy dynamics of the field theory compactified on a three sphere are given by certain non-trivial semi-classical configurations in the moduli space of vacua. We show that this approach is self-consistent and permits one to express most of the dynamics in terms of an effective N=4 SYM dynamics. This has the advantage that some degrees of freedom that move the configurations away from moduli space can be treated perturbatively, unifying the essential low energy dynamics of all of these theories. We show that with this formalism one can compute the energies of strings in the BMN limit in the Klebanov-Witten theory from field theory considerations, matching the functional form of results found using AdS geometry. This paper also presents various other technical results for the semiclassical treatment of superconformal field theories.

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arXiv2007

Giant magnon bound states from strongly coupled N=4 SYM

We calculate in a very simple way the spectrum of giant magnon bound states at strong coupling in N=4 SYM, by utilizing the description of the field theory vacuum in terms of a condensate of eigenvalues of commuting matrices. We further show that these calculations can be understood in terms of the central charge extension that permits the calculation of BPS masses in the Coulomb branch of N=4 SYM. This paper shows further evidence that the strong coupling expansion of the maximally supersymmetric Yang-Mills theory in four dimensions can be done systematically from first principles, without the assumption of integrability.

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arXiv2007

Aspects of open strings in Rindler Space

We study open string configurations in Rindler space suspended from D-branes at finite distance from the Rindler horizon. This is a toy model for strings in the near horizon region of a black hole and has applications for the study of strings configurations of heavy quarks in the AdS/CFT duals of hot field theories, as well as other applications to the study of open strings ending on giant gravitons. We find that this setup produces very similar results to those that have been found in the AdS black hole setup, but it is much more tractable analytically. We also comment on some quantum applications of our studies to the understanding of the spectrum of strings ending on giant gravitons.

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arXiv2007

The Minimal Quiver Standard Model

This paper discusses the minimal quiver gauge theory embedding of the standard model that could arise from brane world type string theory constructions. It is based on the low energy effective field theory of D-branes in the perturbative regime. The model differs from the standard model by the addition of one extra massive gauge boson, and contains only one additional parameter to the standard model: the mass of this new particle. The coupling of this new particle to the standard model is uniquely determined by input from the standard model and consistency conditions of perturbative string theory. We also study some aspects of the phenomenology of this model and bounds on its possible observation at the Large Hadron Collider.

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arXiv2007

A Monte-Carlo study of the AdS/CFT correspondence: an exploration of quantum gravity effects

In this paper we study the AdS/CFT correspondence for N=4 SYM with gauge group U(N), compactified on S^3 in four dimensions using Monte-Carlo techniques. The simulation is based on a particular reduction of degrees of freedom to commuting matrices of constant fields, and in particular, we can write the wave functions of these degrees of freedom exactly. The square of the wave function is equivalent to a probability density for a Boltzman gas of interacting particles in six dimensions. From the simulation we can extract the density particle distribution for each wave function, and this distribution can be interpreted as a special geometric locus in the gravitational dual. Studying the wave functions associated to half-BPS giant gravitons, we are able to show that the matrix model can measure the Planck scale directly. We also show that the output of our simulation seems to match various theoretical expectations in the large N limit and that it captures 1/N effects as statistical fluctuations of the Boltzman gas with the expected scaling. Our results suggest that this is a very promising approach to explore quantum corrections and effects in gravitational physics on AdS spaces.

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arXiv2006

Emergent geometry from q-deformations of N=4 super Yang-Mills

We study BPS states in a marginal deformation of super Yang-Mills on R x S^3 using a quantum mechanical system of q-commuting matrices. We focus mainly on the case where the parameter q is a root of unity, so that the AdS dual of the field theory can be associated to an orbifold of AdS_5x S^5. We show that in the large N limit, BPS states are described by density distributions of eigenvalues and we assign to these distributions a geometrical spacetime interpretation. We go beyond BPS configurations by turning on perturbative non-q-commuting excitations. Considering states in an appropriate BMN limit, we use a saddle point approximation to compute the BMN energy to all perturbative orders in the 't Hooft coupling. We also examine some BMN like states that correspond to twisted sector string states in the orbifold and we show that our geometrical interpretation of the system is consistent with the quantum numbers of the corresponding states under the quantum symmetry of the orbifold.

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arXiv2006

Counting conifolds and Dijkgraaf-Vafa matrix models for three matrices

We study superpotential perturbations of q deformed N=4 Yang-Mills for q a root of unity. This is a special case whose geometry is associated to an orbifold with three lines of codimension two singularities meeting at the origin. We perform field theory perturbations that leave only co-dimension three singularities of conifold type in the geometry. We show that there are two "fractional brane" solutions of the F-term equations for each singularity in the deformed geometry, and that the number of complex deformations of that geometry also matches the number of singularities. This proves that for this case there are no local or non-local obstructions to deformation. We also show that the associated Dijkgraaf-Vafa matrix model has a solvable sector, and that the loop equations in this sector encode the full deformed geometry of the theory.

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arXiv2006

Aspects of emergent geometry in the AdS/CFT context

We study aspects of emergent geometry for the case of orbifold superconformal field theories in four dimensions, where the orbifolds are abelian within the AdS/CFT proposal. In particular, we show that the realization of emergent geometry starting from the N=4 SYM theory in terms of a gas of particles in the moduli space of vacua of a single D3 brane in flat space gets generalized to a gas of particles on the moduli space of the corresponding orbifold conformal field theory (a gas of D3 branes on the orbifold space). Our main purpose is to show that this can be analyzed using the same techniques as in the N=4 SYM case by using the method of images, including the measure effects associated to the volume of the gauge orbit of the configurations. This measure effect gives an effective repulsion between the particles that makes them condense into a non-trivial vacuum configuration, and it is exactly these configurations that lead to the geometry of X in the AdS x X dual field theory

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arXiv2006

A study of open strings ending on giant gravitons, spin chains and integrability

We systematically study the spectrum of open strings attached to half BPS giant gravitons in the N=4 SYM AdS/CFT setup. We find that some null trajectories along the giant graviton are actually null geodesics of AdS_5x S^5, so that we can study the problem in a plane wave limit setup. We also find the description of these states at weak 't Hooft coupling in the dual CFT. We show how the dual description is given by an open spin chain with variable number of sites. We analyze this system in detail and find numerical evidence for integrability. We also discover an interesting instability of long open strings in Ramond-Ramond backgrounds that is characterized by having a continuum spectrum of the string, which is separated from the ground state by a gap. This instability arises from accelerating the D-brane on which the strings end via the Ramond-Ramond field. From the integrable spin chain point of view, this instability prevents us from formulating the integrable structure in terms of a Bethe Ansatz construction.

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