TY - JOUR
T1 - Supersymmetry, chiral symmetry and the generalized BRS transformation in lattice formulations of 4D N=1 SYM
AU - Suzuki, Hiroshi
N1 - Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.
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
VL - 861
SP - 290
EP - 320
JO - Nuclear Physics B
JF - Nuclear Physics B
SN - 0550-3213
IS - 3
ER -