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

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 Schrödinger 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 Schrödinger 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.

We dedicate this paper to the memory of Prof. Rahmi Güven (1948-2019)