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

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.

35 pages; v2 minor corrections, references added

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Cited by in corpus (11)

• Logarithmic Corrections to Kerr Thermodynamics
• ABJM at finite $N$ via 4d supergravity
• 4d N=2 supergravity observables from Nekrasov-like partition functions
• Large $N$ Superconformal Indices for 3d Holographic SCFTs
• Logarithmic correction to black hole entropy in universal low-energy string theory models
• Non-topological logarithmic corrections in minimal gauged supergravity
• Maximally symmetric nuts in 4d $\mathcal{N}=2$ higher derivative supergravity
• Logarithmic correction to the entropy of a Kerr-Newman family of black holes in $U(1{)}^2$-charged STU supergravity models
• Constant maps in equivariant topological strings and geometric modeling of fluxes
• Supersymmetric localization: $\mathcal{N}=(2,2)$ theories on S${}^2$ and AdS${}_2$
• Wrapped $M5$-branes and complex saddle points