Moduli dynamics as a predictive tool for thermal maximally supersymmetric Yang-Mills at large N

TL;DR

This paper explores how the effective moduli theory of large N supersymmetric Yang-Mills can predict the thermodynamics and phase transitions of strongly coupled phases, providing a unified gauge theory perspective on holographic dualities.

Contribution

It introduces a method to use the moduli effective theory at weak coupling to infer properties of strongly coupled phases and phase transitions in large N supersymmetric Yang-Mills.

Findings

Moduli theory encodes thermodynamic quantities of strongly coupled phases.

Predicts phase transitions and geometric factors in thermodynamics.

Provides predictions for local operator behavior in various phases.

Abstract

Maximally supersymmetric (p+1)-dimensional Yang-Mills theory at large N and finite temperature, with possibly compact spatial directions, has a rich phase structure. Strongly coupled phases may have holographic descriptions as black branes in various string duality frames, or there may be no gravity dual. In this paper we provide tools in the gauge theory which give a simple and unified picture of the various strongly coupled phases, and transitions between them. Building on our previous work we consider the effective theory describing the moduli of the gauge theory, which can be computed precisely when it is weakly coupled far out on the Coulomb branch. Whilst for perturbation theory naive extrapolation from weak coupling to strong gives little information, for this moduli theory naive extrapolation from its weakly to its strongly coupled regime appears to encode a surprising amount of information about the various strongly coupled phases. We argue it encodes not only the parametric form of thermodynamic quantities for these strongly coupled phases, but also certain transcendental factors with a geometric origin, and allows one to deduce transitions between the phases. We emphasise it also gives predictions for the behaviour of a large class of local operators in these phases.