Nonholomorphic N=2 terms in N=4 SYM: 1-Loop Calculation in N=2 superspace

TL;DR

This paper computes one-loop nonholomorphic corrections in N=4 SYM using N=2 superspace, revealing how hypermultiplet contributions preserve SU(4) R-symmetry and match N=1 results.

Contribution

It introduces a method to directly calculate hypermultiplet nonholomorphic terms in N=2 superspace for N=4 SYM, enhancing understanding of its effective action.

Findings

Nonholomorphic terms consistent with SU(4) R-symmetry found in N=4 SYM.

Method successfully compares with N=1 abelian subsector calculations.

Effective action includes higher-dimension UV finite corrections.

Abstract

The effective action of N=2 gauge multiplets in general includes higher-dimension UV finite nonholomorphic corrections integrated with the full N=2 superspace measure. By adding a hypermultiplet in the adjoint representation we study the effective action of N=4 SYM. The nonanomalous SU(4) R-symmetry of the classical N=4 theory must be also present in the on-shell effective action, and therefore we expect to find similar nonholomorphic terms for each of the scalars in the hypermultiplet. The N=2 path integral quantization formalism developed in projective superspace allows us to compute these hypermultiplet nonholomorphic terms directly in N=2 superspace. The corresponding gauge multiplet expression can be successfully compared with the result inferred from a N=1 calculation in the abelian subsector.