Harmonicity in N=4 supersymmetry and its quantum anomaly

TL;DR

This paper extends the concept of harmonicity to N=4 supersymmetry, revealing how it governs the moduli dependence of higher-dimensional operators and uncovering an anomaly that affects their recursive structure.

Contribution

It generalizes harmonicity equations to N=4 supersymmetry and demonstrates their role in controlling couplings and revealing anomalies in topological string amplitudes.

Findings

Harmonicity equations control moduli dependence of N=4 operators

Anomaly arises from world-sheet boundary contributions

Recursion relations for non-analytic couplings are derived

Abstract

The holomorphicity property of N=1 superpotentials or of N=2 F-terms involving vector multiplets is generalized to the case of N=4 1/2-BPS effective operators defined in harmonic superspace. The resulting harmonicity equations are shown to control the moduli dependence of the couplings of higher dimensional operators involving powers of the N=4 Weyl superfield, computed by N=4 topological amplitudes. These equations can also be derived on the string side, exhibiting an anomaly from world-sheet boundary contributions that leads to recursion relations for the non-analytic part of the couplings.