Exotic N dependent free energy of black brane solutions from 3D MSYM

TL;DR

This paper derives the N-dependent free energy scaling of black brane solutions in a specific supergravity context using field theory methods, providing insights into their thermodynamic properties.

Contribution

It introduces a field theory derivation of the exotic N dependence of black brane free energy, complementing supergravity results.

Findings

Reproduces N dependence of free energy from field theory

Provides temperature dependence of free energy in low temperature regime

Connects supergravity solutions with field theory analysis

Abstract

Recently, Guarino et al. found that dyonically-gauged N=8 supergravity arises as a consistent truncation of massive type IIA supergravity when the gauge group is chosen to be ISO(7). In particular, they found a critical point of the supergravity that uplifted to the first explicit N = 2 $AdS_4$ massive IIA background. Its free energy was also calculated. Though no black brane solutions for this theory have been constructed yet, we nevertheless expect the free energy of the black brane solutions to scale with the same N dependence as the solution obtained by Guarino et al.. In this note, we will reproduce the exotic N dependence of the free energy of such black brane solutions from field theory at finite temperature using the Smilga-Wiseman approach. The free energy expression thus obtained also tells us about the temperature dependence of free energy of such black brane solutions in a given low temperature regime.