Supersymmetry and superstrata in three dimensions

Abstract

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.

Q-balls meet fuzzballs: non-BPS microstate geometries

“…The supergravity theory of interest is the SO(4, 5) theory described in [21,30]. (Here we will use the notation and conventions of [30].)…”

“…The supergravity theory of interest is the SO(4, 5) theory described in [21,30]. (Here we will use the notation and conventions of [30].) This theory has eight supersymmetries: four two-component spinors in three dimensions, transforming under an SO(4) R-symmetry.…”

“…Specifically, if χ I = 0 then there is a line of critical points with V = V 0 when m IJ has eigenvalues λ, λ, λ −1 , λ −1 for any λ > 0. If the background only involves non-trivial scalar vevs then the critical point only leads to a supersymmetric background for λ = 1 [30]. We will refer to this as the standard, supersymmetric critical point.…”

“…Following [30] we will use a metric signature of (+ − −) and, as noted in [30], one can use coordinate choices to recast the three-dimensional metric in the following form:…”

“…This means that we will put the microstate geometry "in a box" that prevents its thermal decay. Second, we use the recent discovery that a significant family of superstrata are encoded in a consistent truncation of six-dimensional supergravity on S 3 down to a gauged supergravity in three dimensions [21,30]. The inherent power of this consistent truncation is that the complicated dependence of solutions on the S 3 directions is handled entirely by the machinery of the consistent truncation.…”