A compendium of logarithmic corrections in AdS/CFT

Abstract

We study the logarithmic corrections to various CFT partition functions in the context of the AdS${}_4$/CFT${}_3$ correspondence for theories arising on the worldvolume of M2-branes. We utilize four-dimensional gauged supergravity and heat kernel methods and present general expressions for the logarithmic corrections to the gravitational on-shell action and black hole entropy for a number of different supergravity backgrounds. We outline several subtle features of these calculations and contrast them with a similar analysis of logarithmic corrections performed directly in the eleven-dimensional uplift of a given four-dimensional supergravity background. We find results consistent with AdS/CFT provided that the infinite sum over KK modes on the internal space is regularized in a specific manner. This analysis leads to an explicit expression for the logarithmic correction to the Bekenstein-Hawking entropy of large Kerr-Newmann and Reissner-Nordström black holes in AdS${}_4$. Our results also have important implications for effective field theory coupled to gravity in AdS${}_4$ and for the existence of scale-separated AdS${}_4$ vacua in string theory, which come in the form of new constraints on the field content and mass spectrum of matter fields.

v1: 87 pages, 10 tables; v2: Seeley-de Witt coefficients in the presence of non-minimal couplings dictated by supersymmetry are newly addressed in section 5 and following places