Abstract
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.
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Hristov, K., Reys, V. Factorization of log-corrections in AdS4/CFT3 from supergravity localization. J. High Energ. Phys. 2021, 31 (2021). https://doi.org/10.1007/JHEP12(2021)031
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DOI: https://doi.org/10.1007/JHEP12(2021)031