More on BPS solutions of N=2, D=4 gauged supergravity

TL;DR

This paper classifies and refines supersymmetric solutions in N=2, D=4 gauged supergravity, revealing new solutions, symmetries, and connections to known theories, with a complete null case classification and uplift to eleven dimensions.

Contribution

It provides a detailed classification of BPS solutions, introduces a variational principle with PSL(2,R) symmetry, and finds new solutions including kinks and waves, extending previous work.

Findings

Derived PDEs from a variational principle for timelike cases

Discovered new supersymmetric solutions like kinks and waves

Classified all null solutions and uplifted to eleven dimensions

Abstract

We deepen and refine the classification of supersymmetric solutions to N=2, D=4 gauged supergravity obtained in a previous paper. In the case where the Killing vector constructed from the Killing spinor is timelike, it is shown that the nonlinear partial differential equations determining the BPS solutions can be derived from a variational principle. The corresponding action enjoys a solution-generating PSL(2,R) symmetry. In certain subcases the system reduces to different known theories, like two-dimensional dilaton gravity or the dimensionally reduced gravitational Chern-Simons theory. We find new supersymmetric solutions including, among others, kinks that interpolate between two AdS_4 vacua, electrovac waves on anti-Nariai spacetimes, or generalized Robinson-Trautman solutions. In the case where the Killing vector is null, we obtain a complete classification. The one quarter and one half supersymmetric solutions are determined explicitely, and it is shown that the fraction of three quarters of supersymmetry cannot be preserved. Finally, the general lightlike configuration is uplifted to eleven-dimensional supergravity.