Complete Low-Energy Effective action in N=4 SYM: a Direct N=2 Supergraph Calculation

TL;DR

This paper computes the complete one-loop low-energy effective action of N=4 super-Yang-Mills theory using N=2 supergraph techniques, confirming previous algebraic results and providing a comprehensive supersymmetric solution.

Contribution

It presents a direct quantum calculation of the N=4 SYM low-energy effective action, validating earlier algebraic derivations through explicit supergraph methods.

Findings

Confirmed the exact form of the N=4 SYM low-energy effective action.

Demonstrated the dependence on hypermultiplet and gauge fields.

Validated the hidden N=2 supersymmetry in the effective action.

Abstract

Using the covariant N=2 harmonic supergraph techniques we calculate the one-loop low-energy effective action of N=4 super-Yang-Mills theory in Coulomb branch with gauge group SU(2) spontaneously broken down to U(1). The full dependence of the low-energy effective action on both the hypermultiplet and gauge fields is determined. The direct quantum calculation confirms the correctness of the exact N=4 SYM low-energy effective action derived in hep-th/0111062 on the purely algebraic ground by invoking a hidden N=2 supersymmetry which completes the manifest N=2 one to N=4. Our results provide an exhaustive solution to the problem of finding out the exact completely N=4 supersymmetric low-energy effective action for the theory under consideration.