Strongly coupled matrix theory and stochastic quantization: A new approach to holographic dualities

Nick Heller, Vatche Sahakian*

Physical Review D 105, 026012 (2022)

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 the 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.