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Large N BPS states and emergent quantum gravity

David Berenstein

TL;DR

The paper investigates how classical gravity and locality emerge from the strongly coupled N=4 SYM theory in the AdS5×S5 context by restricting to BPS sectors and employing a minisuperspace, gauged matrix model framework. It develops a droplet/hydrodynamic description for 1/2 BPS states and extends to 1/4 and 1/8 BPS sectors, where commuting matrix dynamics lead to E-brane structures whose edge fluctuations map to gravitational excitations. A quantum matrix model for commuting matrices is formulated, yielding ground-state and excited-state eigenfunctions tied to traces and symmetric polynomials, and a coarse-grained, thermodynamic viewpoint that reproduces aspects of LLM-like geometries. The work then discusses topology changes via giant gravitons, the emergence of strings on S^5 as dressed string bits local on the E-brane, and estimates of the string scale at strong coupling, providing a qualitative bridge between CFT dynamics and emergent bulk geometry. Overall, the study offers a cohesive, albeit approximate, roadmap for how emergent spacetime and gravity arise from strongly interacting gauge theory data, highlighting hydrodynamic and topological mechanisms that encode bulk locality and brane dynamics within AdS/CFT.

Abstract

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 show that this is related to a gauged matrix quantum mechanics of commuting matrices. 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 five sphere suggesting that they can be realized as a sigma model on a weakly curved background. In the process we also clarify some aspects of 1/2 BPS states. 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.

Large N BPS states and emergent quantum gravity

TL;DR

The paper investigates how classical gravity and locality emerge from the strongly coupled N=4 SYM theory in the AdS5×S5 context by restricting to BPS sectors and employing a minisuperspace, gauged matrix model framework. It develops a droplet/hydrodynamic description for 1/2 BPS states and extends to 1/4 and 1/8 BPS sectors, where commuting matrix dynamics lead to E-brane structures whose edge fluctuations map to gravitational excitations. A quantum matrix model for commuting matrices is formulated, yielding ground-state and excited-state eigenfunctions tied to traces and symmetric polynomials, and a coarse-grained, thermodynamic viewpoint that reproduces aspects of LLM-like geometries. The work then discusses topology changes via giant gravitons, the emergence of strings on S^5 as dressed string bits local on the E-brane, and estimates of the string scale at strong coupling, providing a qualitative bridge between CFT dynamics and emergent bulk geometry. Overall, the study offers a cohesive, albeit approximate, roadmap for how emergent spacetime and gravity arise from strongly interacting gauge theory data, highlighting hydrodynamic and topological mechanisms that encode bulk locality and brane dynamics within AdS/CFT.

Abstract

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 show that this is related to a gauged matrix quantum mechanics of commuting matrices. 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 five sphere suggesting that they can be realized as a sigma model on a weakly curved background. In the process we also clarify some aspects of 1/2 BPS states. 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.

Paper Structure

This paper contains 13 sections, 62 equations, 8 figures.

Table of Contents

  1. Introduction
  2. The dynamics of 1/2 BPS states
  3. Thermodynamic description of fermion droplets
  4. The chiral ring: BPS states
  5. A quantum matrix model for commuting matrices
  6. Description of the quantum states of the matrix model
  7. Hydrodynamics: the brane description of BPS states.
  8. D-branes and topology changes in BPS geometries
  9. Towards strings on $S^5$ and the string scale
  10. Discussion
  11. Perturbative ${\cal N}=4$ SYM on $S^3$
  12. The operator state correspondence
  13. One loop calculations in $1/8$ BPS configurations

Figures (8)

  • Figure 1: Pictorial comparison of the boson and fermion ground state wave functions
  • Figure 2: Effective radial potential $V(r)$ seen by a probe charge. R is the radius of the droplet. The potential is constant inside the droplet.
  • Figure 3: Distorted edge of a droplet by a coherent state
  • Figure 4: The hole wave function produces a repulsive force from the hole location
  • Figure 5: The quarter BPS membrane with the Hopf fibration: the curves are BPS trajectories on the E-brane, and motion happens along them at the speed of sound.
  • ...and 3 more figures