Supersymmetric Null and Timelike Warped AdS and Strings in D=3, N=2 Gauged Supergravity

TL;DR

This work classifies and constructs supersymmetric solutions of $D=3$, $N=2$ gauged supergravity with a Fayet-Iliopoulos term using Killing spinor bilinears. It uncovers null and timelike warped AdS spacetimes and builds charged string solutions that interpolate between supersymmetric AdS or Minkowski vacua, with horizons appearing at specific vacua and even enabling a supersymmetric null $z$-warped AdS black hole through identifications. The results span sigma-model targets $\mathbb{S}^2$, $\mathbb{H}^2$, and $\mathbb{R}^2$, and include explicit pp-waves, AdS waves, and Kaigorodov-type geometries, enriching the landscape of 3D supersymmetric backgrounds and offering potential holographic applications and RG-flow studies. The paper lays a foundation for further exploration of ungauged limits, higher supersymmetry embeddings, and higher-dimensional origins of these backgrounds.

Abstract

We classify and construct supersymmetric solutions of D=3, N=2 gauged supergravity extended with a Fayet-Iliopoulos term, and null and timelike warped AdS spacetimes are among them. From the first one, it is possible to obtain a well-defined black hole by periodic identification. We also find charged string solutions that interpolate between two supersymmetric AdS or Minkowski extrema of the scalar potential, one of which corresponds to a horizon with a singularity behind it, and the other determines the asymptotic geometry.

Figures (4)

• Figure : $c^2+b=0$ with $b\neq0$
• Figure : $c^2+b=0$ with $b\neq0$
• Figure : $c^2+b\neq0$ with $b\neq0$
• Figure : $c^2+b\neq0$ with $b=0$