The Isometries of Low-Energy Heterotic M-Theory

TL;DR

This paper analyzes the symmetries of the moduli space in low-energy heterotic M-theory with an M5 brane, revealing a non-homogeneous metric invariant under a specific parabolic subgroup of Sp(4,R).

Contribution

It identifies the isometry group of the Kahler moduli-space in heterotic M-theory and characterizes its nonhomogeneous metric structure.

Findings

The isometry group is a non-semisimple maximal parabolic subgroup of Sp(4,R).

The moduli-space is realized as Sp(4,R)/U(2) with a nonhomogeneous invariant metric.

The metric can be derived from field truncations of Sp(8,R)/U(4).

Abstract

We study the effective D=4, N=1 supergravity description of five-dimensional heterotic M-theory in the presence of an M5 brane, and derive the Killing vectors and isometry group for the Kahler moduli-space metric. The group is found to be a non-semisimple maximal parabolic subgroup of Sp(4,R), containing a non-trivial SL(2,R) factor. The underlying moduli-space is then naturally realised as the group space Sp(4,R)/U(2), but equipped with a nonhomogeneous metric that is invariant only under that maximal parabolic group. This nonhomogeneous metric space can also be derived via field truncations and identifications performed on Sp(8,R)/U(4) with its standard homogeneous metric. In a companion paper we use these symmetries to derive new cosmological solutions from known ones.