Doubly-Fluctuating BPS Solutions in Six Dimensions

TL;DR

This paper explores complex six-dimensional BPS solutions in supergravity, revealing new fluctuating microstate geometries that depend on multiple variables and directions, advancing the understanding of superstratum constructions.

Contribution

It introduces novel six-dimensional BPS solutions with two-variable fluctuations, providing insights into microstate geometries and superstratum development.

Findings

Found smooth microstate geometries with multi-variable dependence.

Demonstrated solutions depend on the entire T^2 structure.

Connected solutions to superstratum construction.

Abstract

We analyze the BPS solutions of minimal supergravity coupled to an anti-self-dual tensor multiplet in six dimensions and find solutions that fluctuate non-trivially as a function of two variables. We consider families of solutions coming from KKM monopoles fibered over Gibbons-Hawking metrics or, equivalently, non-trivial T^2 fibrations over an R3 base. We find smooth microstate geometries that depend upon many functions of one variable, but each such function depends upon a different direction inside the T^2 so that the complete solution depends non-trivially upon the whole T^2 . We comment on the implications of our results for the construction of a general superstratum.