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

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