A one-loop test of quantum supergravity

The partition function on the three-sphere of ABJM theory and its generalizations has, at large N, a universal, subleading logarithmic term. Inspired by the success of one-loop quantum gravity for computing the logarithmic corrections to black hole entropy, we try to reproduce this universal term by a one-loop calculation in Euclidean 11-dimensional supergravity on AdS(4) x X-7. We find perfect agreement between the results of ABJM theory and the 11-dimensional supergravity.