Anomalous N=2 superconformal Ward identities

TL;DR

This paper explores anomalous Ward identities in N=2 superconformal theories, revealing new identities, solutions, and connections to hypermultiplet moduli spaces, with implications for mirror symmetry in 3D N=4 theories.

Contribution

It introduces a new anomalous N=2 superconformal Ward identity related to hypermultiplet sectors and finds solutions under certain symmetry assumptions.

Findings

Identified a new anomalous Ward identity for hypermultiplet low-energy effective actions.

Found solutions to the new Ward identity involving SU(2) monopole moduli-space metrics.

Supported mirror symmetry between Coulomb and Higgs branches in 3D N=4 theories.

Abstract

The N=2 superconformal Ward identities and their anomalies are discussed in N=2 superspace (including N=2 harmonic superspace), at the level of the low-energy effective action (LEEA) in four-dimensional N=2 supersymmetric field theories. The (first) chiral N=2 supergravity compensator is related to the known N=2 anomalous Ward identity in the N=2 (abelian) vector mulitplet sector. As regards the hypermultiplet LEEA given by the N=2 non-linear sigma-model (NLSM), a new anomalous N=2 superconformal Ward identity is found, whose existence is related to the (second) analytic compensator in N=2 supergravity. The celebrated solution of Seiberg and Witten is known to obey the (first) anomalous Ward identity in the Coulomb branch. We find a few solutions to the new anomalous Ward identity, after making certain assumptions about unbroken internal symmetries. Amongst the N=2 NLSM target space metrics governing the hypermultiplet LEEA are the SU(2)-Yang-Mills-Higgs monopole moduli-space metrics that can be encoded in terms of the spectral curves (Riemann surfaces), similarly to the Seiberg-Witten-type solutions. After a dimensional reduction to three spacetime dimensions (3d), our results support the mirror symmetry between the Coulomb and Higgs branches in 3d, N=4 gauge theories.