AdS$_3$ solutions with exceptional supersymmetry

TL;DR

This paper constructs and analyzes unique AdS$_3$ solutions in type IIA supergravity with exceptional supersymmetry, revealing new geometries with specific internal spaces and flux configurations.

Contribution

It presents the first explicit analytic solutions realizing exceptional superalgebras F(4) and G(3) in type IIA supergravity, with detailed internal geometries and fluxes.

Findings

Two unique solutions with exceptional supersymmetry are found.

Internal space is a six-sphere fibred over an interval with O8-plane.

Numerical solutions with G(2) symmetry and various sources are also provided.

Abstract

Among the possible superalgebras that contain the AdS$_3$ isometries, two interesting possibilities are the exceptional $F(4)$ and $G(3)$. Their R-symmetry is respectively SO(7) and $G_2$, and the amount of supersymmetry ${\cal N}=8$ and ${\cal N}=7$. We find that there exist two (locally) unique solutions in type IIA supergravity that realize these superalgebras, and we provide their analytic expressions. In both cases, the internal space is obtained by a round six-sphere fibred over an interval, with an O8-plane at one end. The R-symmetry is the symmetry group of the sphere; in the $G(3)$ case, it is broken to $G_2$ by fluxes. We also find several numerical ${\cal N}=1$ solutions with $G_2$ flavor symmetry, with various localized sources, including O2-planes and O8-planes.