2021/07/31 by Kiril Hristov, Valentin Reys · 1 citation
Physics and Astronomy · Mathematics · #hep-th #math.DG
paper · pdf · doi:10.1007/jhep12(2021)031
35 pages; v2 minor corrections, references added
arxiv created 2021/08/04 · arxiv updated 2022/01/05
We use the Atiyah-Singer index theorem to derive the general form of the one-loop corrections to observables in asymptotically anti-de Sitter (AdS4) supersymmetric backgrounds of abelian gauged supergravity. Using the method of supergravity localization combined with the factorization of the supergravity action on fixed points (NUTs) and fixed two-manifolds (Bolts) we show that an analogous factorization takes place for the one-loop determinants of supergravity fields. This allows us to propose a general fixed-point formula for the logarithmic corrections to a large class of supersymmetric partition functions in the large N expansion of a given 3d dual theory. The corrections are uniquely fixed by some simple topological data pertaining to a particular background in the form of its regularized Euler characteristic χ, together with a single dynamical coefficient that counts the underlying degrees of freedom of the theory.