Rotating AdS$_3 \times$S$^3$ and Dyonic Strings from 3-Dimensions

TL;DR

This paper analyzes supersymmetric solutions in a specific 3D gauged supergravity, deriving new rotating and dyonic string solutions through uplift to higher dimensions, revealing novel geometries with scale invariance and string distributions.

Contribution

It provides a comprehensive Killing spinor analysis of a 3D gauged supergravity and constructs three new supersymmetric solutions with physical relevance.

Findings

Found null warped AdS3 with Schrödinger symmetry.

Derived rotating dyonic string solutions in 6D.

Produced a distribution of dyonic strings from a domain wall uplift.

Abstract

We make a general Killing spinor analysis of a particular $D=3, \, N=4$ gauged supergravity that comes from a consistent S$^3$ reduction of $D=6, \, N=(1,0)$ supergravity coupled to a single chiral tensor multiplet. We then focus on its supersymmetric solutions with a null Killing vector and find three new ones. Two of these, namely the null warped AdS$_3$ (also known as the Schr\"odinger spacetime) and the charged domain wall solutions, admit non-trivial gauge fields which give rise to rotating solutions in 6-dimensions. The uplift of the first one produces an interesting AdS$_3 \times$S$^3$ background with a non-trivial rotation in the $U(1)$ fiber direction of the S$^3$ which retains the Schr\"odinger scale invariance that the seed solution has. The second one leads to the well-known rotating dyonic string solution. Finally, the uplift of the third one, which is a domain wall solution with no gauge fields, results in a distribution of dyonic strings.