Thermodynamics of black M-branes from SCFTs

We discuss thermodynamics of N M2-branes at strong coupling from the ABJM theory by employing the Smilga-Wiseman method, which explains the black Dp-brane thermodynamics from the maximally supersymmetric U(N) Yang-Mills theories through a field theory analysis. As a result we obtain the free energy of the ABJM theory ~ N3/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \sqrt{k}{T^3} $\end{document}, which is consistent with the prediction from the eleven-dimensional supergravity. We also estimate the free energy of N M5-branes by assuming some natural properties of the 6d superconformal field theory. Remarkably we obtain the free energy ~ N3T6, which is consistent again with the supergravity prediction. This result might illuminate the low energy field theory description of the multiple M5-branes.