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