Supergravity Solutions from Floating Branes

TL;DR

This paper introduces a new class of non-BPS supergravity solutions using a floating-brane Ansatz, expanding the known solution space and connecting to BPS and almost-BPS solutions through spectral flow.

Contribution

It develops a comprehensive method to construct non-BPS supergravity solutions from Euclidean Einstein-Maxwell bases, including explicit solutions with Israel-Wilson metrics.

Findings

Derived a new class of non-BPS solutions

Explicit solutions describing non-BPS D6 and anti-D6 branes

Established spectral flow relations between different solution classes

Abstract

We solve the equations of motion of five-dimensional ungauged supergravity coupled to three U(1) gauge fields using a floating-brane Ansatz in which the electric potentials are directly related to the gravitational warp factors. We find a new class of non-BPS solutions, that can be obtained linearly starting from an Euclidean four-dimensional Einstein-Maxwell base. This class - the largest known so far - reduces to the BPS and almost-BPS solutions in certain limits. We solve the equations explicitly when the base space is given by the Israel-Wilson metric, and obtain solutions describing non-BPS D6 and anti-D6 branes kept in equilibrium by flux. We also examine the action of spectral flow on solutions with an Israel-Wilson base and show that it relates these solutions to almost-BPS solutions with a Gibbons-Hawking base.