Supersymmetry and superstrata in three dimensions

We analyze the supersymmetry transformations of gauged SO(4) supergravity coupled to extra hypermultiplets in three dimensions, and find large families of smooth BPS solutions that preserve four supersymmetries. These BPS solutions are part of the consistent truncation of some families of six-dimensional superstrata. From the three-dimensional perspective, these solutions give rise to smoothly-capped BTZ geometries. We show how the twisting of the spin connection, the holomorphy of the fields, and the Chern-Simons connections all play an essential role in the existence of these supersymmetric solutions. This paper also closes the circle on the consistent truncation of superstrata, showing precisely how every feature of the superstratum enters into the three-dimensional BPS structure.

Automated summary

The paper analyzes the supersymmetry transformations of gauged SO(4) supergravity coupled to extra hypermultiplets in three dimensions, identifying large families of smooth BPS solutions that preserve four supersymmetries. These solutions lead to smoothly-capped BTZ geometries from a three-dimensional perspective, with the twisting of the spin connection, holomorphy of the fields, and Chern-Simons connections playing crucial roles in their existence. The paper also demonstrates how the consistent truncation of superstrata closes the circle, showing the incorporation of every feature of the superstratum into the three-dimensional BPS structure.