Towards lattice simulation of the gauge theory duals to black holes and hot strings

TL;DR

This work investigates the feasibility of lattice simulations for strongly coupled gauge theories that are holographically dual to black holes and hot strings, focusing on the 4-supercharge Yang–Mills quantum mechanics as a tractable warm-up to the 16-supercharge case. The authors compare naive and manifestly supersymmetric lattice actions, analytically argue that naive discretization should recover continuum SUSY without fine tuning, and validate this with Monte Carlo simulations in both zero- and finite-temperature settings. They observe consistency between discretizations under periodic boundary conditions and demonstrate a single deconfined phase at nonzero temperature in the 4-supercharge theory, with observables obeying large-N scaling up to N=12. The results offer encouraging evidence that lattice techniques can capture the thermodynamics of holographically dual black holes and hot strings, and they set the stage for extending these methods to the more challenging 16-supercharge theory, where a Pfaffian phase may pose additional hurdles. Overall, the study provides methodological advances and substantive thermodynamic insights relevant to gauge/gravity duality and nonperturbative quantum gravity models.

Abstract

A generalization of the AdS/CFT conjecture postulates a duality between IIA string theory and 16 supercharge Yang-Mills quantum mechanics in the large N 't Hooft limit. At low temperatures string theory describes black holes, whose thermodynamics may hence be studied using the dual quantum mechanics. This quantum mechanics is strongly coupled which motivates the use of lattice techniques. We argue that, contrary to expectation, the theory when discretized naively will nevertheless recover continuum supersymmetry as the lattice spacing is sent to zero. We test these ideas by studying the 4 supercharge version of this Yang-Mills quantum mechanics in the 't Hooft limit. We use both a naive lattice action and a manifestly supersymmetric action. Using Monte Carlo methods we simulate the Euclidean theories, and study the lattice continuum limit, for both thermal and non-thermal periodic boundary conditions, confirming continuum supersymmetry is recovered for the naive action when appropriate. We obtain results for the thermal system with N up to 12. These favor the existence of a single deconfined phase for all non-zero temperatures. These results are an encouraging indication that the 16 supercharge theory is within reach using similar methods and resources.