Non-abelian gravity and antisymmetric tensor gauge theory

August , 1997 Non - Abelian Gravity and Antisymmetric Tensor Gauge Theory

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 generali...

Non - Abelian Gravity and Antisymmetric Tensor Gauge Theory

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 generali...

Stochastic Quantization of Non-Abelian Antisymmetric Tensor Fields

A Stochastic Quantization Method (in short, SQM)l) was first introduced by Parisi and Wu) as the third quantization method of gauge theories. Their statement is as follows: In this scheme there is no need to fix the gauge degrees of freedom, i.e., no need to introduce any artificial auxiliary fields (ghost and multiplier fields). It is the main advantage of the SQM. It is essentially governed b...

Antisymmetric Tensor Gauge Fields on S4

Topological Aspects in Non - Abelian Gauge Theory

We discuss the BRST cohomology and exhibit a connection between the Hodge decomposition theorem and the topological properties of a two dimensional free non-Abelian gauge theory having no interaction with matter fields. The topological nature of this theory is encoded in the vanishing of the Laplacian operator when equations of motion are exploited. We obtain two sets of topological invariants ...