Non-Abelian Gravity and Antisymmetric Tensor Gauge Theory

TL;DR

This paper develops a non-abelian extension of a gravity theory coupled with a 2-form gauge field and dilaton, exploring its mathematical properties and relevance to string theory and M-theory.

Contribution

It introduces a non-abelian generalisation of a gravity and gauge field theory, connecting it to string theory and brane dynamics.

Findings

The non-abelian theory is local with a vector pre-potential.

In the abelian limit, the curvature exhibits self-duality or SU(n) holonomy.

The theory relates to the effective action of (2,1) strings and coincident branes.

Abstract

A non-abelian generalisation of a theory of gravity coupled to a 2-form gauge field and a dilaton is found, in which the metric and 3-form field strength are Lie algebra-valued. In the abelian limit, the curvature with torsion is self-dual in four dimensions, or has SU(n) holonomy in $2n$ dimensions. The coupling to self-dual Yang-Mills fields in 4 dimensions, or their higher dimensional generalisation, is discussed. The abelian theory is the effective action for (2,1) strings, and the non-abelian generalisation is relevant to the study of coincident branes in the (2,1) string approach to M-theory. The theory is local when expressed in terms of a vector pre-potential.