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

Research output: Contribution to journalArticle

20 Citations (Scopus)

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

Fingerprint

supersymmetry
formulations
symmetry
continuums
operators
Yang-Mills theory
broken symmetry
perturbation theory
fermions
coefficients

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.

In: Nuclear Physics B, Vol. 861, No. 3, 21.08.2012, p. 290-320.

Research output: Contribution to journalArticle

@article{479c193cd5c648159578f1b4e948d935,
title = "Supersymmetry, chiral symmetry and the generalized BRS transformation in lattice formulations of 4D N=1 SYM",
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.",
author = "Hiroshi Suzuki",
year = "2012",
month = "8",
day = "21",
doi = "10.1016/j.nuclphysb.2012.04.008",
language = "English",
volume = "861",
pages = "290--320",
journal = "Nuclear Physics B",
issn = "0550-3213",
publisher = "Elsevier",
number = "3",

}

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 -