On Low-Energy Effective Action of Noncommutative Hypermultiplet Model

TL;DR

This paper analyzes the one-loop effective action of a noncommutative hypermultiplet model in harmonic superspace, revealing how quantum corrections generate multiple couplings and affect UV/IR mixing depending on the representation.

Contribution

It introduces a detailed calculation of the one-loop effective action for noncommutative hypermultiplets, including the generation of multiple couplings and the impact of UV/IR mixing in different representations.

Findings

Both coupling constants are generated by 1-loop quantum corrections.

No UV/IR mixing occurs in the fundamental representation.

Leading contributions in the adjoint representation relate to the U(1) phase.

Abstract

We consider the noncommutative hypermultiplet model within harmonic superspace approach. The 1-loop four-point contributions to the effective action of selfinteracting q-hypermultiplet are computed. This model has two coupling constants instead of a single one in commutative case. It is shown that both these coupling constants are generated by 1-loop quantum corrections in the model of q-hypermultiplet interacting with vector multiplet. The holomorphic effective action of q-hypermultiplet in external gauge superfield is calculated. For the fundamental representation there is no UV/IR-mixing and the holomorphic potential is a star-product generalization of a standard commutative one. For the adjoint representation of U(N) gauge group the leading contributions to the holomorphic effective action are given by the terms respecting for the UV/IR-mixing which are related to U(1) phase of U(N) group.