On Strongly Coupled Matrix Theory and Stochastic Quantization: A New Approach to Holographic Dualities

TL;DR

This paper introduces a novel approach combining stochastic quantization and variational methods to analyze strongly coupled matrix theories, successfully computing correlators and phase transitions relevant to holographic dualities.

Contribution

It presents a new analytical framework for studying strong coupling regimes in matrix theories using stochastic variational techniques, advancing understanding of holographic dualities.

Findings

Computed two-point functions at all couplings matching lattice results

Captured confinement-deconfinement phase transition at strong coupling

Demonstrated potential for exploring emergent geometry in holography

Abstract

Stochastic quantization provides an alternate approach to the computation of quantum observables, by stochastically sampling phase space in a path integral. Furthermore, the stochastic variational method can provide analytical control over the strong coupling regime of a quantum field theory -- provided one has a decent qualitative guess at the form of certain observables at strong coupling. In the context of the holographic duality, the strong coupling regime of a Yang-Mills theory can capture gravitational dynamics. This can provide enough insight to guide a stochastic variational ansatz. We demonstrate this in the bosonic Banks-Fischler-Shenker-Susskind Matrix theory. We compute a two-point function at all values of coupling using the variational method showing agreement with lattice numerical computations and capturing the confinement-deconfinement phase transition at strong coupling. This opens up a new realm of possibilities for exploring the holographic duality and emergent geometry.