Linearizing the BPS Equations with Vector and Tensor Multiplets

TL;DR

This paper demonstrates how BPS equations in six-dimensional supergravity with vector and tensor multiplets can be reduced to linear differential equations, facilitating the construction of new microstate geometries and superstrata.

Contribution

It introduces a method to linearize BPS equations in supergravity with vector and tensor multiplets, enabling new solutions and microstate geometries.

Findings

Reduction of BPS equations to linear form

Construction of new microstate geometries

Potential development of new superstrata

Abstract

We analyse the BPS equations of $\mathcal{N} = (1,0)$ supergravity theory in six dimensions coupled to a vector and tensor multiplet. We show how these BPS equations can be reduced to a set of linear differential equations. This system is triangular in that each layer of equations, while linear, is quadratically sourced by the solutions of the previous layers. We examine several explicit examples and discuss the construction of new families of microstate geometries. We expect that the result presented here will open up new branches of superstrata in which the momentum is encoded in a new class of charge carriers.