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Factorization of log-corrections in AdS$_4$/CFT$_3$ from supergravity localization

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arxiv 2107.12398 v2 pith:V3DUQ6J5 submitted 2021-07-26 hep-th math.DG

Kiril Hristov , Valentin Reys This is my paper · ORCID
classification hep-thmath.DG
keywords supergravitycorrectionsfactorizationfixedformgenerallargelocalization
verification ladder T0 review T1 audit T2 compute T3 formal
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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 (AdS$_4$) 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 $\chi$, together with a single dynamical coefficient that counts the underlying degrees of freedom of the theory.

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Cited by 4 Pith papers

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    hep-th 2026-07 conditional novelty 8.0 of 10

    Relative equivariant localization of quantum M-theory reproduces the Airy partition functions of ABJM and toric Calabi-Yau M2-brane theories, up to prefactor and non-perturbative corrections.

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    hep-th 2024-11 conditional novelty 6.0 of 10

    A perturbatively exact ABJM partition function on Seifert manifolds is matched to Euclidean AdS-Taub-Bolt supergravity, including N^{1/2} and log N corrections.

  4. Type IIB Supergravity Action and Holography

    hep-th 2026-03 accept novelty 5.5 of 10

    A milder topological correction to the PST Type IIB action yields non-vanishing on-shell values matching holography for Lunin-Maldacena and AdS4 S-fold backgrounds.

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