The Cardy-limit index for M2-brane theories gives a large-N free energy scaling as N^(3/2) that, after a Legendre transform, matches the entropy of BPS black holes in AdS4 x S7.
The Conformal Anomaly of M5-Branes
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abstract
We show that the conformal anomaly for N M5-branes grows like $N^3$. The method we employ relates Coulomb branch interactions in six dimensions to interactions in four dimensions using supersymmetry. This leads to a relation between the six-dimensional conformal anomaly and the conformal anomaly of N=4 Yang-Mills. Along the way, we determine the structure of the four derivative interactions for the toroidally compactified (2,0) theory, while encountering interesting novelties in the structure of the six derivative interactions.
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Quantum vortices, M2-branes and black holes
The Cardy-limit index for M2-brane theories gives a large-N free energy scaling as N^(3/2) that, after a Legendre transform, matches the entropy of BPS black holes in AdS4 x S7.