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

TL;DR

This work advances the systematic classification of BPS solutions in $N=2$, $D=4$ gauged supergravity by thoroughly analyzing timelike and lightlike Killing vectors, revealing a variational principle in the timelike sector with a $PSL(2,R)$ symmetry and connections to reduced 2D dilaton gravity and gravitational Chern–Simons theory. It constructs and catalogs numerous new supersymmetric geometries, including kink interpolations between AdS$_4$ vacua, electrovac waves on anti-Nariai backgrounds, and generalized Robinson–Trautman and Kundt waves, while providing a complete lightlike-case classification and explicit spinor structures. The study also demonstrates an uplift of the general lightlike solutions to eleven dimensions, suggesting a broader M-theory interpretation and potential holographic implications of the PSL(2,R) structure. Overall, the results enhance the toolkit for generating and interpreting BPS backgrounds in AdS/CFT contexts and motivate deeper exploration of the underlying geometric and holographic frameworks.

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.