Observables in topological Yang-Mills theory and the Gribov problem

Abstract

Topological Yang-Mills theory (TYMT) is one of topological quantum field theories, which were proposed and developed by Witten1. Topological invariants obtained from TYMT are Donaldson polynomials2. TYMT has BRST symmetry and observables are defined to be BRST cohomology classes. We can prove that correlation functions of observables are independent of a metric on the underlying four dimensional space-time and, therefore, topological invariants. Witten identified these correlation functions with Donaldson polynomials. Thus, Donaldson polynomials appear as BRST cohomology class (observables) of TYMT and we have a path integral representation of Donaldson polynomials.