BPS-like potential for compactifications of heterotic M-theory?

TL;DR

This paper investigates whether the action of heterotic M-theory can be expressed in a BPS-like form after compactification on SU(3) structure manifolds, revealing it is only possible for specific cases.

Contribution

It demonstrates that a BPS-like rewriting of the heterotic M-theory action is generally not possible, except for particular compactification types.

Findings

BPS-like form is not generally obtainable for heterotic M-theory compactifications.

Only certain SU(3) structure compactifications allow a BPS-like rewriting.

The scalar curvature can be expressed in terms of SU(3) structure forms for specific cases.

Abstract

We analyze the possibility to rewrite the action of Horava-Witten theory in a BPS-like form, which means that it is given as a sum of squares of the supersymmetry conditions. To this end we compactify the theory on a seven dimensional manifold of SU(3) structure and rewrite the scalar curvature of the compactification manifold in terms of the SU(3) structure forms. This shows that a BPS-like form cannot be obtained in general, but only for certain types of compactifications.