5D Black Holes and Non-linear Sigma Models

TL;DR

This paper extends the dimensional reduction approach for analyzing stationary solutions in 5D supergravity to include gauged cases, exploring BPS solutions and their wave functions.

Contribution

It generalizes the reduction procedure to 5D gauged supergravity and studies the algebra of BPS constraints for various black hole solutions.

Findings

Identification of gauging in 3D from 5D supergravity

Analysis of BPS constraints for specific black holes

Derivation of semi-classical wave functions

Abstract

Stationary solutions of 5D supergravity with U(1) isometry can be efficiently studied by dimensional reduction to three dimensions, where they reduce to solutions to a locally supersymmetric non-linear sigma model. We generalize this procedure to 5D gauged supergravity, and identify the corresponding gauging in 3D. We pay particular attention to the case where the Killing spinor is non constant along the fibration, which results, even for ungauged supergravity in 5D, in an additional gauging in 3D, without introducing any extra potential. We further study SU(2)\times U(1) symmetric solutions, which correspond to geodesic motion on the sigma model (with potential in the gauged case). We identify and study the algebra of BPS constraints relevant for the Breckenridge-Myers-Peet-Vafa black hole, the Gutowski-Reall black hole and several other BPS solutions, and obtain the corresponding radial wave functions in the semi-classical approximation.