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We study the logarithmic corrections to various CFT partition functions in the context of the AdS₄/CFT₃ 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-Nordstr\"om black holes in AdS₄. Our results also have important implications for effective field theory coupled to gravity in AdS₄ and for the existence of scale-separated AdS₄ vacua in string theory, which come in the form of new constraints on the field content and mass spectrum of matter fields.
Bobev et al. (Thu,) studied this question.