TY - JOUR

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

AU - Suzuki, Hiroshi

N1 - Funding Information:
I am indebted to Yusuke Taniguchi for helpful discussions at various stages of the present work and to Michael G. Endres for a careful reading of the manuscript and useful comments. This work was initiated during the CERN Theory Institute, “Future directions in lattice gauge theory—LGT10”. I would like to thank the workshop organizers, especially, Poul H. Damgaard and Martin Lüscher, for their kind hospitality. My thanks also goes to Ting-Wai Chiu for the hospitality extended to me at the Center for Theoretical Sciences, Taipei, Taiwan, R.O.C., where the latter part of this work was carried out. This work is supported in part by a Grant-in-Aid for Scientific Research , 22340069 and 23540330 .

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.

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U2 - 10.1016/j.nuclphysb.2012.04.008

DO - 10.1016/j.nuclphysb.2012.04.008

M3 - Article

AN - SCOPUS:84860252617

SN - 0550-3213

VL - 861

SP - 290

EP - 320

JO - Nuclear Physics B

JF - Nuclear Physics B

IS - 3

ER -