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

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.