Large N BPS states and emergent quantum gravity

By D. Berenstein. 2005

217 citations recorded by the source corpus.

This paper provides a heuristic derivation of how classical gravitational physics in the AdS/CFT correspondence appears from the strong dynamics of the N = 4 SYM theory in a systematic way. We do this in a minisuperspace approximation by studying 1/8 BPS configurations. We can show that our description matches the semiclassical physics of 1/8 BPS states in supergravity. We also provide a heuristic description of how massive strings appear in the geometry, and how at strong 't Hooft coupling they become local on the S 5 suggesting that they can be realized as a sigma model on a weakly curved background. We show that the dynamics of 1/8 BPS dynamics of N = 4 SYM on a round S 3 can be reduced to that of a matrix model for commuting matrices. Including measure factors, we show that this effective dynamics is related to bosons living on a six dimensional phase space with repulsive interactions. Because of these interactions, we can argue that on the ground state the bosons assemble themselves on a spherical shell in the shape of a round five sphere. This sphere will be identified with the S 5 in the AdS dual geometry. To do this, we first define a precise way to coarse grain the dynamics. We use half BPS configurations as a toy model for this coarse graining, and we can reproduce the droplet picture of these half BPS states systematically. The droplet appears as the saddle point approximation of a statistical ensemble related to the square of the wave function of the eigenvalues of a complex matrix. This procedure is also applied to the set of 1/8 BPS configurations to extract the geometry, giving an analog of the droplet picture of half BPS states for the case of 1/8 BPS configurations. We also have a conjectured realization of some 1/8 BPS giant graviton wave functions in the dynamics, which captures all 1/8 BPS giant gravitons constructed by Mikhailov. This leads to a lot of different topology changes which can be treated heuristically.

Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c374b5637bdaf3fabe2554682ee32069381a5b23

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Citations in the corpus

An Index for 4 Dimensional Super Conformal Theories (2005, background): “3) Further discussion on these 1/8 BPS states can be found in [10].”
Supersymmetric states of N=4 Yang-Mills from giant gravitons (2006, unknown): “31”
Comments on quantum gravity and entanglement (2009, background): “(21)The recent work of Berenstein [35] on the emergence geometry from matrix degrees of freedom may be helpful here.”
SUPERCONFORMAL FIELD THEORIES (2005, unknown): “Recently there has been a lot of progress in understanding the AdS-CFT correspondence [1, 2, 3, 4].”
Three-dimensional N=6 SCFT's and their membrane dynamics (2008, methodology): “Similar considerations haven been used in [63, 64] to address classically the problem of N = 1 superconformal field theories in four dimensions, a setup that we will follow closely (see also [65, 66] for related”
Static patch solipsism: conformal symmetry of the de Sitter worldline (2011, background): “The SL(2, R) invariant state may be AdS2 or AdS3, with the Sd−1 emerging as a description of the ground state in the spirit of [60, 61].”
Lectures on holographic methods for condensed matter physics (2009, background): “The emergence of first principles of spacetime geometry from field theory is far from understood (preliminary ideas can be found in, for instance, [23]).”
Giant gravitons—with strings attached (I) (2007, unknown): “For an attempt to recover gravitational thermodynamics see [23]; for an attempt to understand spacetime as an emergent phenomenon see[24].”
Emergent spacetime and holographic CFTs (2011, result): “The general approach of our paper is closely related to various other works which appeared in the past [5], [6], [7], [8], [9].”
AdS 3 solutions of IIB supergravity from D3-branes (2005, background): “The relevant matrix model description of the eigenvalue dynamics for N = 4, D = 4 Yang-Mills theory has been discussed in [ 17 ].”
The library of Babel: on the origin of gravitational thermodynamics (2005, background): “While this paper was being completed we became aware of several other works on related topics [47, 59, 60].”
Black holes as effective geometries (2008, background): “Probe solutions (giant gravitons) preserving 1/8 of the supersymmetry were studied in [137,138,139,140,141] and the back-reaction of such probes was worked out in [142,143].”
Diagonal multi-matrix correlators and BPS operators in N=4 SYM (2007, background): “Following [1] (see also [40, 41, 42]), the Hamiltonian is H = ∑”