RECORD
Supersymmetry on the lattice and the Leibniz rule
High Energy Physics - Theory · Submitted 10 May 2002
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We show that this model reproduces continuum theory in the limit $a\to 0$ up to any finite order in perturbation theory; in this sense all the supersymmetry breaking terms induced by the failure of the Leibniz rule are irrelevant.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
The major obstacle to a supersymmetric theory on the lattice is the failure of the Leibniz rule. We analyze this issue by using the Wess-Zumino model and a general Ginsparg-Wilson operator, which is local and free of species doublers. We point out that the Leibniz rule could be maintained on the lattice if the generic momentum $k_{\mu}$ carried by any field variable satisfies $|ak_{\mu}|<\delta$ in the limit $a\to 0$ for arbitrarily small but finite $\delta$. This condition is expected to be satisfied generally if the theory is finite perturbatively, provided that discretization does not induce further symmetry breaking. We thus first render the continuum Wess-Zumino model finite by applying the higher derivative regularization which preserves supersymmetry. We then put this theory on the lattice, which preserves supersymmetry except for a breaking in interaction terms by the failure of the Leibniz rule. By this way, we define a lattice Wess-Zumino model which maintains the basic properties such as $U(1)\times U(1)_{R}$ symmetry and holomorphicity. We show that this model reproduces continuum theory in the limit $a\to 0$ up to any finite order in perturbation theory; in this sense all the supersymmetry breaking terms induced by the failure of the Leibniz rule are irrelevant. We then suggest that this discretization may work to define a low energy effective theory in a non-perturbative way.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The major obstacle to a supersymmetric theory on the lattice is the failure of the Leibniz rule. | background 0.99 | 0.07 | 0.04 | asserted 1.00 |
| s1 | We analyze this issue by using the Wess-Zumino model and a general Ginsparg-Wilson operator, which is local and free of species doublers. | method 0.89 | 0.90 | 0.03 | asserted 0.98 |
| s2 | We point out that the Leibniz rule could be maintained on the lattice if the generic momentum $k_{\mu}$ carried by any field variable satisfies $|ak_{\mu}|<\delta$ in the limit $a\to 0$ for arbitrarily small but finite $\delta$. | result 0.91 | 0.77 | 0.36 | hedged possibility 1.00 |
| s3 | This condition is expected to be satisfied generally if the theory is finite perturbatively, provided that discretization does not induce further symmetry breaking. | interpretation 0.88 | 0.18 | 0.09 | hedged possibility 0.97 |
| s4 | We thus first render the continuum Wess-Zumino model finite by applying the higher derivative regularization which preserves supersymmetry. | method 0.97 | 0.90 | 0.04 | asserted 1.00 |
| s5 | We then put this theory on the lattice, which preserves supersymmetry except for a breaking in interaction terms by the failure of the Leibniz rule. | method 0.65 | 0.92 | 0.11 | asserted 1.00 |
| s6 | By this way, we define a lattice Wess-Zumino model which maintains the basic properties such as $U(1)\times U(1)_{R}$ symmetry and holomorphicity. | contribution 0.58 | 0.89 | 0.09 | asserted 1.00 |
| s7 | We show that this model reproduces continuum theory in the limit $a\to 0$ up to any finite order in perturbation theory; in this sense all the supersymmetry breaking terms induced by the failure of the Leibniz rule are irrelevant. | result 0.92 | 0.94 | 0.58 | asserted 1.00 |
| s8 | We then suggest that this discretization may work to define a low energy effective theory in a non-perturbative way. | future work 0.89 | 0.43 | 0.22 | hedged possibility 1.00 |
What was examined, and what was not
- arXiv listing abstract v3
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
The major obstacle to a supersymmetric theory on the lattice is the failure of the Leibniz rule. We analyze this issue by using the Wess-Zumino model and a general Ginsparg-Wilson operator, which is local and free of species doublers. We point out that the Leibniz rule could be maintained on the lattice if the generic momentum $k_{\mu}$ carried by any field variable satisfies $|ak_{\mu}|<\delta$ in the limit $a\to 0$ for arbitrarily small but finite $\delta$. This condition is expected to be satisfied generally if the theory is finite perturbatively, provided that discretization does not induce further symmetry breaking. We thus first render the continuum Wess-Zumino model finite by applying the higher derivative regularization which preserves supersymmetry. We then put this theory on the lattice, which preserves supersymmetry except for a breaking in interaction terms by the failure of the Leibniz rule. By this way, we define a lattice Wess-Zumino model which maintains the basic properties such as $U(1)\times U(1)_{R}$ symmetry and holomorphicity. We show that this model reproduces continuum theory in the limit $a\to 0$ up to any finite order in perturbation theory; in this sense all the supersymmetry breaking terms induced by the failure of the Leibniz rule are irrelevant. We then suggest that this discretization may work to define a low energy effective theory in a non-perturbative way.
Human review
References
How the literature uses it
9 arXiv papers cite this in 12 sentences
Papers citing it · 10 sentences without a confident label
Cites it as background 2 papers
-
In this Letter, we propose a nonperturbative Euclidean formulation of a dimensional reduction of the Wess-Zumino (WZ) model [ref] to three and two dimensions.[We assume that the Kähler potential is the flat one, $Φ^†Φ$, and the superpotential is cubic in the three-dimensional model, so that the model is ultraviolet (UV) finite.] On a nonperturbative formulation of the WZ model, there exist many preceding studies, mostly based on spacetime or spatial lattices [ref] .[In Sec. 2.2, we will clarify the relation of our proposal to a lattice formulation in Ref. [ref] that is based on the SLAC derivative [ref] .] (For exact renormalization group approaches to the WZ model, see Refs. [ref] .) The desired features of our present proposal are: (I) full supersymmetry (SUSY) as well as the translational invariance and all global symmetries are manifestly preserved, (II) it is amenable to nonperturba
Supersymmetric nonperturbative formulation of the WZ model in lower dimensions · Introduction · 0.90
-
There are some later developments [ref] .
Formulation of Supersymmetry on a Lattice as a Representation of a Deformed Superalgebra · Introduction · 0.96
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.