### Abstract

An N = 1 / 2 supergravity in four Euclidean spacetime dimensions, coupled to both vector- and scalar-multiplet matter, is constructed for the first time. We begin with the standard N = (1, 1) conformally extended supergravity in four Euclidean dimensions, and freeze out the graviphoton field strength to an arbitrary (fixed) self-dual field (the so-called C-deformation). Though a consistency of such procedure with local supersymmetry is not guaranteed, we find a simple consistent set of algebraic constraints that reduce the local supersymmetry by 3/4 and eliminate the corresponding gravitini. The final field theory (after the superconformal gauge-fixing) has the residual local N = (0, frac(1, 2)) or just N = 1 / 2 supersymmetry with only one chiral gravitino as the corresponding gauge field. Our theory is not 'Lorentz'-invariant because of the non-vanishing self-dual graviphoton vacuum expectation value, which is common to the C-deformed N = 1 / 2 rigidly supersymmetric field theories constructed in a non-anticommutative superspace.

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

Pages (from-to) | 495-511 |

Number of pages | 17 |

Journal | Nuclear Physics B |

Volume | 794 |

Issue number | 3 |

DOIs | |

Publication status | Published - 11 May 2008 |

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### Keywords

- Gravi-photon
- Supergravity

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*794*(3), 495-511. https://doi.org/10.1016/j.nuclphysb.2007.10.020

**N = 1 / 2 supergravity with matter in four Euclidean dimensions.** / Hatanaka, Tomoya; Ketov, Sergei V.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 794, no. 3, pp. 495-511. https://doi.org/10.1016/j.nuclphysb.2007.10.020

}

TY - JOUR

T1 - N = 1 / 2 supergravity with matter in four Euclidean dimensions

AU - Hatanaka, Tomoya

AU - Ketov, Sergei V.

PY - 2008/5/11

Y1 - 2008/5/11

N2 - An N = 1 / 2 supergravity in four Euclidean spacetime dimensions, coupled to both vector- and scalar-multiplet matter, is constructed for the first time. We begin with the standard N = (1, 1) conformally extended supergravity in four Euclidean dimensions, and freeze out the graviphoton field strength to an arbitrary (fixed) self-dual field (the so-called C-deformation). Though a consistency of such procedure with local supersymmetry is not guaranteed, we find a simple consistent set of algebraic constraints that reduce the local supersymmetry by 3/4 and eliminate the corresponding gravitini. The final field theory (after the superconformal gauge-fixing) has the residual local N = (0, frac(1, 2)) or just N = 1 / 2 supersymmetry with only one chiral gravitino as the corresponding gauge field. Our theory is not 'Lorentz'-invariant because of the non-vanishing self-dual graviphoton vacuum expectation value, which is common to the C-deformed N = 1 / 2 rigidly supersymmetric field theories constructed in a non-anticommutative superspace.

AB - An N = 1 / 2 supergravity in four Euclidean spacetime dimensions, coupled to both vector- and scalar-multiplet matter, is constructed for the first time. We begin with the standard N = (1, 1) conformally extended supergravity in four Euclidean dimensions, and freeze out the graviphoton field strength to an arbitrary (fixed) self-dual field (the so-called C-deformation). Though a consistency of such procedure with local supersymmetry is not guaranteed, we find a simple consistent set of algebraic constraints that reduce the local supersymmetry by 3/4 and eliminate the corresponding gravitini. The final field theory (after the superconformal gauge-fixing) has the residual local N = (0, frac(1, 2)) or just N = 1 / 2 supersymmetry with only one chiral gravitino as the corresponding gauge field. Our theory is not 'Lorentz'-invariant because of the non-vanishing self-dual graviphoton vacuum expectation value, which is common to the C-deformed N = 1 / 2 rigidly supersymmetric field theories constructed in a non-anticommutative superspace.

KW - Gravi-photon

KW - Supergravity

UR - http://www.scopus.com/inward/record.url?scp=38849203013&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38849203013&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2007.10.020

DO - 10.1016/j.nuclphysb.2007.10.020

M3 - Article

VL - 794

SP - 495

EP - 511

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 3

ER -