Abstract

Abstract Supersymmetric terms in the effective action of $ \mathcal{N}=2 $ supergravity in four dimensions are generically classified into chiral-superspace integrals and full-superspace integrals. For a theory of $ \mathcal{N}=2 $ vector multiplets coupled to supergravity, a special class of couplings is given by chiral-superspace integrals that are governed by a holomorphic prepotential function. The quantum entropy of BPS black holes in such theories depends on the prepotential according to a known integral formula. We show, using techniques of localization, that a large class of full-superspace integrals in the effective action of $ \mathcal{N}=2 $ supergravity do not contribute to the quantum entropy of BPS black holes at any level in the derivative expansion. Our work extends similar results for semi-classical supersymmetric black hole entropy, and goes towards providing an explanation of why the prepotential terms capture the exact microscopic quantum black hole entropy.

Highlights

  • The gravitational theory with boundary conditions set by the AdS2 attractor configuration arising in the near-horizon region of the black hole

  • We show, using techniques of localization, that a large class of full-superspace integrals in the effective action of N = 2 supergravity do not contribute to the quantum entropy of BPS black holes at any level in the derivative expansion

  • We review the fact that the semi-classical black hole entropy does not change on adding these full-superspace terms to the effective action

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Summary

Quantum black hole entropy and localization

We first briefly review the BPS black hole solutions in the N = 2 supergravity theory that we are interested in. We review the concept of quantum entropy as applied to these black holes. We summarize the computation of the exact quantum entropy of these black holes using the localization formalism

Semi-classical black hole entropy
Quantum black hole entropy
Computation of quantum entropy using localization
Full-superspace integrals and the semi-classical entropy
A large class of full-superspace integral Lagrangians
Non-renormalization of semi-classical entropy
Full-superspace integrals and the quantum entropy
The localizing solutions
Evaluation of the full-superspace Lagrangians
D2φD2φ 16
Discussion
A Some details of the off-shell multiplets and the Euclidean continuation
B The quartic and cubic pieces of the general full-superspace Lagrangian
Full Text
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