### Abstract

In the context of the lattice regularization of the four-dimensional N=1 supersymmetric Yang-Mills theory (4D N=1 SYM), we formulate a generalized BRS transformation that treats the gauge, supersymmetry (SUSY), translation and axial U(1) (U(1) _{A}) transformations in a unified way. A resultant Slavnov-Taylor identity or the Zinn-Justin equation gives rise to a strong constraint on the quantum continuum limit of symmetry breaking terms with the lattice regularization. By analyzing the implications of the constraint on operator-mixing coefficients in the SUSY and the U(1) _{A} Ward-Takahashi (WT) identities, we prove to all orders of perturbation theory in the continuum limit that, (i) the chiral symmetric limit implies the supersymmetric limit and, (ii) a three-fermion operator that might potentially give rise to an exotic breaking of the SUSY WT identity does not emerge. In previous literature, only a naive or incomplete treatment on these points can be found. Our results provide a solid theoretical basis for lattice formulations of the 4D N=1 SYM.

Original language | English |
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Pages (from-to) | 290-320 |

Number of pages | 31 |

Journal | Nuclear Physics B |

Volume | 861 |

Issue number | 3 |

DOIs | |

Publication status | Published - Aug 21 2012 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Cite this

**Supersymmetry, chiral symmetry and the generalized BRS transformation in lattice formulations of 4D N=1 SYM.** / Suzuki, Hiroshi.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Supersymmetry, chiral symmetry and the generalized BRS transformation in lattice formulations of 4D N=1 SYM

AU - Suzuki, Hiroshi

PY - 2012/8/21

Y1 - 2012/8/21

N2 - In the context of the lattice regularization of the four-dimensional N=1 supersymmetric Yang-Mills theory (4D N=1 SYM), we formulate a generalized BRS transformation that treats the gauge, supersymmetry (SUSY), translation and axial U(1) (U(1) A) transformations in a unified way. A resultant Slavnov-Taylor identity or the Zinn-Justin equation gives rise to a strong constraint on the quantum continuum limit of symmetry breaking terms with the lattice regularization. By analyzing the implications of the constraint on operator-mixing coefficients in the SUSY and the U(1) A Ward-Takahashi (WT) identities, we prove to all orders of perturbation theory in the continuum limit that, (i) the chiral symmetric limit implies the supersymmetric limit and, (ii) a three-fermion operator that might potentially give rise to an exotic breaking of the SUSY WT identity does not emerge. In previous literature, only a naive or incomplete treatment on these points can be found. Our results provide a solid theoretical basis for lattice formulations of the 4D N=1 SYM.

AB - In the context of the lattice regularization of the four-dimensional N=1 supersymmetric Yang-Mills theory (4D N=1 SYM), we formulate a generalized BRS transformation that treats the gauge, supersymmetry (SUSY), translation and axial U(1) (U(1) A) transformations in a unified way. A resultant Slavnov-Taylor identity or the Zinn-Justin equation gives rise to a strong constraint on the quantum continuum limit of symmetry breaking terms with the lattice regularization. By analyzing the implications of the constraint on operator-mixing coefficients in the SUSY and the U(1) A Ward-Takahashi (WT) identities, we prove to all orders of perturbation theory in the continuum limit that, (i) the chiral symmetric limit implies the supersymmetric limit and, (ii) a three-fermion operator that might potentially give rise to an exotic breaking of the SUSY WT identity does not emerge. In previous literature, only a naive or incomplete treatment on these points can be found. Our results provide a solid theoretical basis for lattice formulations of the 4D N=1 SYM.

UR - http://www.scopus.com/inward/record.url?scp=84860252617&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84860252617&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2012.04.008

DO - 10.1016/j.nuclphysb.2012.04.008

M3 - Article

AN - SCOPUS:84860252617

VL - 861

SP - 290

EP - 320

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 3

ER -