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

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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 languageEnglish
Pages (from-to)290-320
Number of pages31
JournalNuclear Physics B
Volume861
Issue number3
DOIs
Publication statusPublished - Aug 21 2012
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics

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