### Abstract

The component structure of a generic N = 1/2 supersymmetric nonlinear sigma-model (NLSM) defined in the four-dimensional (Euclidean) nonanticommutative (NAC) superspace is investigated in detail. The most general NLSM is described in terms of arbitrary Kähler potential, and chiral and antichiral superpotentials. The case of a single chiral superfield gives rise to splitting of the NLSM potentials, whereas the case of several chiral superfields results in smearing (or fuzziness) of the NLSM potentials, while both effects are controlled by the auxiliary fields. We eliminate the auxiliary fields by solving their algebraic equations of motion, and demonstrate that the results are dependent upon whether the auxiliary integrations responsible for the fuzziness are performed before or after elimination of the auxiliary fields. There is no ambiguity in the case of splitting, i.e., for a single chiral superfield. Fully explicit results are derived in the case of the N = 1/2 supersymmetric NAC-deformed CP^{n} NLSM in four dimensions. Here we find another surprise that our results differ from the N = 1/2 supersymmetric CP^{n} NLSM derived by the quotient construction from the N = 1/2 supersymmetric NAC-deformed gauge theory. We conclude that an N = 1/2 supersymmetric deformation of a generic NLSM from the NAC superspace is not unique.

Original language | English |
---|---|

Pages (from-to) | 481-493 |

Number of pages | 13 |

Journal | Nuclear Physics B |

Volume | 726 |

Issue number | 3 |

DOIs | |

Publication status | Published - 24 Oct 2005 |

### Fingerprint

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*726*(3), 481-493. https://doi.org/10.1016/j.nuclphysb.2005.08.024

**N =1/2 supersymmetric four-dimensional nonlinear σ-models from nonanticommutative superspace.** / Hatanaka, Tomoya; Ketov, Sergei V.; Kobayashi, Yoshishige; Sasaki, Shin.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 726, no. 3, pp. 481-493. https://doi.org/10.1016/j.nuclphysb.2005.08.024

}

TY - JOUR

T1 - N =1/2 supersymmetric four-dimensional nonlinear σ-models from nonanticommutative superspace

AU - Hatanaka, Tomoya

AU - Ketov, Sergei V.

AU - Kobayashi, Yoshishige

AU - Sasaki, Shin

PY - 2005/10/24

Y1 - 2005/10/24

N2 - The component structure of a generic N = 1/2 supersymmetric nonlinear sigma-model (NLSM) defined in the four-dimensional (Euclidean) nonanticommutative (NAC) superspace is investigated in detail. The most general NLSM is described in terms of arbitrary Kähler potential, and chiral and antichiral superpotentials. The case of a single chiral superfield gives rise to splitting of the NLSM potentials, whereas the case of several chiral superfields results in smearing (or fuzziness) of the NLSM potentials, while both effects are controlled by the auxiliary fields. We eliminate the auxiliary fields by solving their algebraic equations of motion, and demonstrate that the results are dependent upon whether the auxiliary integrations responsible for the fuzziness are performed before or after elimination of the auxiliary fields. There is no ambiguity in the case of splitting, i.e., for a single chiral superfield. Fully explicit results are derived in the case of the N = 1/2 supersymmetric NAC-deformed CPn NLSM in four dimensions. Here we find another surprise that our results differ from the N = 1/2 supersymmetric CPn NLSM derived by the quotient construction from the N = 1/2 supersymmetric NAC-deformed gauge theory. We conclude that an N = 1/2 supersymmetric deformation of a generic NLSM from the NAC superspace is not unique.

AB - The component structure of a generic N = 1/2 supersymmetric nonlinear sigma-model (NLSM) defined in the four-dimensional (Euclidean) nonanticommutative (NAC) superspace is investigated in detail. The most general NLSM is described in terms of arbitrary Kähler potential, and chiral and antichiral superpotentials. The case of a single chiral superfield gives rise to splitting of the NLSM potentials, whereas the case of several chiral superfields results in smearing (or fuzziness) of the NLSM potentials, while both effects are controlled by the auxiliary fields. We eliminate the auxiliary fields by solving their algebraic equations of motion, and demonstrate that the results are dependent upon whether the auxiliary integrations responsible for the fuzziness are performed before or after elimination of the auxiliary fields. There is no ambiguity in the case of splitting, i.e., for a single chiral superfield. Fully explicit results are derived in the case of the N = 1/2 supersymmetric NAC-deformed CPn NLSM in four dimensions. Here we find another surprise that our results differ from the N = 1/2 supersymmetric CPn NLSM derived by the quotient construction from the N = 1/2 supersymmetric NAC-deformed gauge theory. We conclude that an N = 1/2 supersymmetric deformation of a generic NLSM from the NAC superspace is not unique.

UR - http://www.scopus.com/inward/record.url?scp=25844464327&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=25844464327&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2005.08.024

DO - 10.1016/j.nuclphysb.2005.08.024

M3 - Article

VL - 726

SP - 481

EP - 493

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 3

ER -