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Supersymmetry, chiral symmetry and the generalized BRS transformation in lattice formulations of 4D $\mathcal{N}=1$ SYM
High Energy Physics - Lattice · Submitted 13 Feb 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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The abstract, sentence by sentence
In the context of the lattice regularization of the four-dimensional $\mathcal{N}=1$ supersymmetric Yang--Mills theory (4D $\mathcal{N}=1$ 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 $\mathcal{N}=1$ SYM.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In the context of the lattice regularization of the four-dimensional $\mathcal{N}=1$ supersymmetric Yang--Mills theory (4D $\mathcal{N}=1$ 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. | contribution 0.91 | 0.95 | 0.06 | asserted 1.00 |
| s1 | 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. | result 0.46 | 0.74 | 0.07 | asserted 1.00 |
| s2 | 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. | result 0.99 | 0.96 | 0.87 | asserted 1.00 |
| s3 | In previous literature, only a naive or incomplete treatment on these points can be found. | gap 1.00 | 0.04 | 0.02 | asserted 0.98 |
| s4 | Our results provide a solid theoretical basis for lattice formulations of the 4D $\mathcal{N}=1$ SYM. | interpretation 0.98 | 0.49 | 0.18 | asserted 1.00 |
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Original abstract
In the context of the lattice regularization of the four-dimensional $\mathcal{N}=1$ supersymmetric Yang--Mills theory (4D $\mathcal{N}=1$ 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 $\mathcal{N}=1$ SYM.
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References
How the literature uses it
12 arXiv papers cite this in 16 sentences
Papers citing it · 12 sentences without a confident label
Cites it as support 1 paper
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This is not what we expect and we thus assume its absence: [equation] As shown in Ref. [ref] by utilizing the generalized BRS transformation, this is actually the case at least to all orders in the perturbation theory.
Ferrara--Zumino supermultiplet and the energy-momentum tensor in the lattice formulation of 4D $\mathcal{N}=1$ SYM · Lattice SUSY current and a renormalized SUSY WT relation · 0.99
Cites it as background 3 papers
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In this section, we recall how the proposal of Ref. [ref] that SUSY in the lattice formulation of 4D $𝒩=1$ SYM is restored with an appropriate tuning of the gluino mass $M$ is understood in terms of the SUSY WT relation [ref] .
Ferrara--Zumino supermultiplet and the energy-momentum tensor in the lattice formulation of 4D $\mathcal{N}=1$ SYM · Lattice SUSY current and a renormalized SUSY WT relation · 0.85
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As discussed in Ref. [ref] , SUSY gauge theories can be studied on the lattice.
Latest lattice results of N=1 supersymmetric Yang-Mills theory with some topological insights · Chiral symmetry, SUSY, and continuum limit · 0.83
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See Refs. [ref] for theoretical studies on this issue and Ref. [ref] for a recent actual numerical study in the four-dimensional (4D) $𝒩=1$ super Yang–Mills (SYM) theory.
Gradient flow representation of the four-dimensional $\mathcal{N}=2$ super Yang--Mills supercurrent · Introduction and summary · 0.96
What it cites · 3 sentences without a confident label
Cites as background 10 papers
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Some related works are Refs. [ref] .[Ref. [ref] is discussing a possible implication of the lattice BRS invariance (in the non-perturbative level) in supersymmetric gauge theories.]
Supersymmetric gauge theories on the lattice: Pfaffian phases and the Neuberger 0/0 problem · Introduction · 0.98
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Classified by the method for simulating the gaugino or gluino, a fermionic superpartner of the gauge boson, Refs. [ref] use the Wilson fermion [ref] (see Ref. [ref] for a very readable review), Refs. [ref] employ the domain-wall fermion [ref] and, most recently, Ref. [ref] uses the overlap fermion [ref] .
Lattice super-Yang-Mills using domain wall fermions in the chiral limit · Introduction · 0.89
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Classified by the method for simulating the gaugino or gluino, a fermionic superpartner of the gauge boson, Refs. [ref] use the Wilson fermion [ref] (see Ref. [ref] for a very readable review), Refs. [ref] employ the domain-wall fermion [ref] and, most recently, Ref. [ref] uses the overlap fermion [ref] .
Dynamical simulation of lattice 4d N=1 SYM · Introduction · 0.89
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