Multi-Instantons, Supersymmetry and Topological Field Theories

TL;DR

This paper explores how instanton effects in N=2 Super Yang-Mills theories can be computed via constrained instantons or topological twisting, linking supersymmetry, topological field theories, and the Seiberg-Witten effective action.

Contribution

It demonstrates the equivalence of instanton calculations using constrained instantons and topological field theory methods, and expresses Seiberg-Witten coefficients as integrals over moduli space.

Findings

Equivalence of instanton computation methods.

Seiberg-Witten coefficients as total derivatives.

BRST operator relates supersymmetry and gauge variations.

Abstract

In this letter we argue that instanton-dominated Green's functions in N=2 Super Yang-Mills theories can be equivalently computed either using the so-called constrained instanton method or making reference to the topological twisted version of the theory. Defining an appropriate BRST operator (as a supersymmetry plus a gauge variation), we also show that the expansion coefficients of the Seiberg-Witten effective action for the low-energy degrees of freedom can be written as integrals of total derivatives over the moduli space of self-dual gauge connections.