Covariantly constant forms on torsionful geometries from world-sheet and spacetime perspectives

TL;DR

This paper explores the symmetries of supersymmetric sigma models on special holonomy target spaces, introducing Nijenhuis forms and analyzing their implications for geometries relevant to heterotic supergravity.

Contribution

It introduces Nijenhuis forms arising from covariantly constant forms and studies structure group reductions in torsionful geometries from both world-sheet and spacetime perspectives.

Findings

Nijenhuis forms generate new symmetries in sigma models.

Covariantly constant one-forms lead to additional symmetries.

Reductions of structure groups are linked to supersymmetry in supergravity solutions.

Abstract

The symmetries of two-dimensional supersymmetric sigma models on target spaces with covariantly constant forms associated to special holonomy groups are analysed. It is shown that each pair of such forms gives rise to a new one, called a Nijenhuis form, and that there may be further reductions of the structure group. In many cases of interest there are also covariantly constant one-forms which also give rise to symmetries. These geometries are of interest in the context of heterotic supergravity solutions and the associated reductions are studied from a spacetime point of view via the Killing spinor equations.