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

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.