On Mass-Deformed N=4 Supersymmetric Yang-Mills Theory

TL;DR

This paper constructs the n-instanton action for N=4 supersymmetric Yang-Mills with SU(2) gauge group, computes the quantum modulus at one-instanton level, and discusses discrepancies with Seiberg-Witten solutions.

Contribution

It provides the explicit n-instanton action for N=4 SYM and analyzes the quantum modulus, highlighting potential modifications to existing Seiberg-Witten relations.

Findings

Calculated the quantum modulus u at 1-instanton level.

Found a discrepancy with Seiberg-Witten's proposed exact solution.

Suggested possible modifications to the relation between u and the elliptic curve parameter.

Abstract

We construct the n-instanton action for the above model with gauge group SU(2), as a function of the collective coordinates of the general self-dual configurations of Atiyah, Drinfeld, Hitchin and Manin (ADHM). We calculate the quantum modulus u = <Tr(A^2)> at the 1-instanton level, and find a discrepancy with Seiberg and Witten's proposed exact solution. As in related models (N=2, N_F=3 or 4), this discrepancy may be resolved by modifying their proposed relation between $\tilde u$ (the parameter in the elliptic curve) and u.