The Non-Split Scalar Coset in Supergravity Theories

TL;DR

This paper explores the structure and formulations of non-split scalar cosets in supergravity, analyzing their symmetries, dualizations, and relations to string theory compactifications.

Contribution

It provides a detailed study of the symmetric space sigma model for non-split scalar cosets, including dualization and first order formulations for non-compact real forms.

Findings

Dualization and local first order formulation for non-split scalar cosets.

Comparison with scalar cosets in heterotic string compactifications.

Analysis of different coset parametrizations and their implications.

Abstract

The general non-split scalar coset of supergravity theories is discussed.The symmetric space sigma model is studied in two equivalent formulations and for different coset parametrizations.The dualisation and the local first order formulation is performed for the non-split scalar coset G/K when the rigid symmetry group G is a real form of a non-compact semisimple Lie group (not necessarily split) and the local symmetry group K is G's maximal compact subgroup.A comparison with the scalar cosets arising in the T^{10-D}-compactification of the heterotic string theory in ten dimensions is also mentioned.