All solutions of the localization equations for N=2 quantum black hole entropy

TL;DR

This paper derives the complete set of bosonic solutions to localization equations for N=2 supergravity black hole entropy, including all field fluctuations, revealing the structure of the localization manifold.

Contribution

It extends previous results by incorporating fluctuations of all off-shell supergravity fields, providing the most general solutions for supersymmetric black hole entropy calculations.

Findings

Solutions are labeled by n_v+1 parameters for auxiliary field fluctuations.

Additional fields introduce an SU(2) triplet of one-forms and a scalar function.

The work completes the characterization of the localization manifold for these black holes.

Abstract

We find the most general bosonic solution to the localization equations describing the contributions to the quantum entropy of supersymmetric black holes in four-dimensional N=2 supergravity coupled to n_v vector multiplets. This requires the analysis of the BPS equations of the corresponding off-shell supergravity (including fluctuations of the auxiliary fields) with AdS2 \times S2 attractor boundary conditions. Our work completes and extends the results of arXiv:1012.0265 that were obtained for the vector multiplet sector, to include the fluctuations of all the fields of the off-shell supergravity. We find that, when the auxiliary SU(2) gauge field strength vanishes, the most general supersymmetric configuration preserving four supercharges is labelled by n_v+1 real parameters corresponding to the excitations of the conformal mode of the graviton and the scalars of the n_v vector multiplets. In the general case, the localization manifold is labelled by an additional SU(2) triplet of one-forms and a scalar function.