Quantum vortices, M2-branes and black holes

We study the partition functions of BPS vortices and magnetic monopole operators, in gauge theories describing N M2-branes. In particular, we explore two closely related methods to study the Cardy limit of the index on S-2 x R. The first method uses the factorization of this index to vortex partition functions, while the second one uses a continuum approximation for the monopole charge sums. Monopole condensation confines most of the N-2 degrees of freedom except N-3/2 of them, even in the high temperature deconfined phase. The resulting large N free energy statistically accounts for the Bekenstein-Hawking entropy of large BPS black holes in AdS(4) x S-7. Our Cardy free energy also suggests a finite N version of the N-3/2 degrees of freedom.