N=2 SYM Action as a BRST Exact Term, Topological Yang Mills and Instantons

TL;DR

This paper demonstrates that N=2 Super Yang Mills action can be expressed as a BRST exact term and relates it to topological Yang Mills theory through specific field redefinitions, revealing an intrinsic connection between physical and topological aspects.

Contribution

It introduces a novel nonanalytical gauge fermion involving inverse supersymmetry ghosts, enabling a direct derivation of topological Yang Mills from N=2 SYM without twisting.

Findings

N=2 SYM action is BRST exact with a nonanalytical gauge fermion.

Topological Yang Mills theory can be obtained via field redefinitions from N=2 SYM.

The physical and topological interpretations of N=2 SYM are interconnected.

Abstract

By constructing a nilpotent extended BRST operator $\bs$ that involves the N=2 global supersymmetry transformations of one chirality, we show that the standard N=2 off-shell Super Yang Mills Action can be represented as an exact BRST term $\bs \Psi$, if the gauge fermion $\Psi$ is allowed to depend on the inverse powers of supersymmetry ghosts. By using this nonanalytical structure of the gauge fermion (via inverse powers of supersymmetry ghosts), we give field redefinitions in terms of composite fields of supersymmetry ghosts and N=2 fields and we show that Witten's topological Yang Mills theory can be obtained from the ordinary Euclidean N=2 Super Yang Mills theory directly by using such field redefinitions. In other words, TYM theory is obtained as a change of variables (without twisting). As a consequence it is found that physical and topological interpretations of N=2 SYM are intertwined together due to the requirement of analyticity of global SUSY ghosts. Moreover, when after an instanton inspired truncation of the model is used, we show that the given field redefinitions yield the Baulieu-Singer formulation of Topological Yang Mills.