### 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.

Original language | English |
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Pages (from-to) | 119-138 |

Number of pages | 20 |

Journal | Nuclear Physics B |

Volume | 582 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - 28 Aug 2000 |

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### Keywords

- 11.30.Pb
- Anomaly
- Supergravity
- Supersymmetry

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*582*(1-3), 119-138. https://doi.org/10.1016/S0550-3213(00)00266-2