### 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 |
---|---|

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 |

### Fingerprint

### 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

**Anomalous N=2 superconformal Ward identities.** / Ketov, Sergei V.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 582, no. 1-3, pp. 119-138. https://doi.org/10.1016/S0550-3213(00)00266-2

}

TY - JOUR

T1 - Anomalous N=2 superconformal Ward identities

AU - Ketov, Sergei V.

PY - 2000/8/28

Y1 - 2000/8/28

N2 - 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.

AB - 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.

KW - 11.30.Pb

KW - Anomaly

KW - Supergravity

KW - Supersymmetry

UR - http://www.scopus.com/inward/record.url?scp=0034726215&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034726215&partnerID=8YFLogxK

U2 - 10.1016/S0550-3213(00)00266-2

DO - 10.1016/S0550-3213(00)00266-2

M3 - Article

AN - SCOPUS:0034726215

VL - 582

SP - 119

EP - 138

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 1-3

ER -