BRST Cohomology of N=2 Super-Yang-Mills Theory in 4D

TL;DR

This paper explores the BRST cohomology of four-dimensional N=2 super-Yang-Mills theory using a twisted algebra approach, linking gauge invariants to the action and paving the way for algebraic proofs of quantum properties.

Contribution

It introduces a method to compute BRST cohomology in N=2 SYM using twisted algebra and establishes a key relationship between gauge invariants and the action.

Findings

Derived the BRST cohomology classes using twisted N=2 algebra

Established a relationship between $tr\phi^2$ and the N=2 Yang-Mills action

Provided groundwork for algebraic proof of one-loop beta function exactness

Abstract

The BRST cohomology of the N=2 supersymmetric Yang-Mills theory in four dimensions is discussed by making use of the twisted version of the N=2 algebra. By the introduction of a set of suitable constant ghosts associated to the generators of N=2, the quantization of the model can be done by taking into account both gauge invariance and supersymmetry. In particular, we show how the twisted N=2 algebra can be used to obtain in a straightforward way the relevant cohomology classes. Moreover, we shall be able to establish a very useful relationship between the local gauge invariant polynomial $tr\phi^2$ and the complete N=2 Yang-Mills action. This important relation can be considered as the first step towards a fully algebraic proof of the one-loop exactness of the N=2 beta function.