Non Abelian TQFT and scattering of self dual field configuration

TL;DR

This paper introduces a non-abelian topological quantum field theory derived from 4D self-dual Yang-Mills fields, quantizing the phase space via holomorphic structures on Riemann surfaces, and explores its relation to topological gravity.

Contribution

It presents a novel non-abelian TQFT for self-dual fields, with an exact quantization of the phase space using stable vector bundles, linking to topological gravity.

Findings

Exact quantization of the phase space achieved.

Static solutions identified as Dirac monopoles.

Connection established between the TQFT and topological gravity.

Abstract

A non-abelian topological quantum field theory describing the scattering of self-dual field configurations over topologically non-trivial Riemann surfaces, arising from the reduction of 4-dim self-dual Yang-Mills fields, is introduced. It is shown that the phase space of the theory can be exactly quantized in terms of the space of holomorphic structures over stable vector bundles of degree zero over Riemann surfaces. The Dirac monopoles are particular static solutions of the field equations. Its relation to topological gravity is discussed.