Codimension-2 brane solutions of maximal supergravities in 9, 8, and 7 dimensions

TL;DR

This paper constructs explicit codimension-2 BPS brane solutions in maximal supergravities across 9, 8, and 7 dimensions, revealing their connections to higher-dimensional theories like F-theory and M-theory.

Contribution

It provides new explicit solutions in lower-dimensional supergravities, linking them to holomorphic functions and higher-dimensional string/M-theory frameworks.

Findings

In D=9, solutions match 10D cases with a holomorphic function.

In D=8, solutions involve two holomorphic functions, related to T^2 x T^2 compactification.

In D=7, solutions relate to M-theory on Calabi-Yau, with a simplified case also described by two holomorphic functions.

Abstract

We construct codimension-2 BPS brane solutions in $D=9,8,7$ maximal supergravities by solving Killing spinor equations. We assume the Poincare invariance along the worldvolume and vanishing gauge fields, and determine the metric and the scalar fields. The solution in $D=9$ is essentially the same as the ten-dimensional one, which is specified by a holomorphic function in the transverse space. For $D=8$, the solution is specified by two holomorphic functions, and regarded as $T^2\times T^2$ compactification of F-theory. For $D=7$, we find that the solution can be interpreted as M-theory on Calabi-Yau, and under an additional assumption a solution is specified by two holomorphic functions.