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

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 other observables in these phases.

A proposal of the gauge theory description of the small Schwarzschild black hole in AdS5 × S5

“…Furthermore, if we use the duality to understand the quantum gravitational aspects of black holes, we have 1 The authors would like to thank Jorge Santos for the clarification. 2 Analytic approaches for deriving nontrivial temperature dependence have been discussed in [6][7][8][9].…”

Thermodynamics of intersecting black branes from interacting elementary branes

“…Then we can investigate the microstates of these branes similarly. Furthermore the phase transitions between these branes [16] could be understood microscopically in a fashion of [4]. In such a way, we can study the various black brane dynamics in string theory through our proposal.…”

“…Then we can understand the thermodynamics of the branes in terms of the gauge theories. Not only that, the effective action might be useful to estimate several quantities in the gauge theories even if they are not able to be calculated through the gravity [4]. In the case of the intersecting brane systems, much more varieties of supersymmetric gauge theories appear on the branes than the single-species brane case.…”

“…This proposal works in the various BPS branes in superstring and M-theory, and we can explain the black hole thermodynamics of the black brane solutions through the effective actions for these branes similar to (1.1) [2][3][4]. (The related studies have been done in [5][6][7][8][9].)…”

“…4 Suppose that this term is balanced to the term in the third line which is from L 2 (3.5) due to the virial theorem, we obtain the relation between v and r as…”