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Leutwyler-Smilga sum rules for Ginsparg-Wilson lattice fermions

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F. Farchioni

High Energy Physics - Lattice · Submitted 23 Feb 1999

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We argue that lattice QCD with Ginsparg-Wilson fermions satisfies the Leutwyler-Smilga sum rules for the eigenvalues of the chiral Dirac operator.

how it is stated · asserted 0.58 read the record →

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arXiv IDhep-lat/9902029 (version 2)
Pith IDYSFDUIT5, Pith's permanent record of this paper and its review
CitationF. Farchioni. "Leutwyler-Smilga sum rules for Ginsparg-Wilson lattice fermions." arXiv:hep-lat/9902029 (1999). https://pith.science/paper/YSFDUIT5
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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.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,035 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.76 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.49 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We argue that lattice QCD with Ginsparg-Wilson fermions satisfies the Leutwyler-Smilga sum rules for the eigenvalues of the chiral Dirac operator. The result is obtained in the one flavor case, by rephrasing Leutwyler and Smilga's original analysis for the finite volume partition function. This is a further evidence that Ginsparg-Wilson fermions, even if breaking explicitly the chirality on the lattice in accordance to the Nielsen-Ninomiya theorem, mimic the main features of the continuum theory related to chiral symmetry.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We argue that lattice QCD with Ginsparg-Wilson fermions satisfies the Leutwyler-Smilga sum rules for the eigenvalues of the chiral Dirac operator. result 0.89 0.66 0.95 asserted 0.58
s1 The result is obtained in the one flavor case, by rephrasing Leutwyler and Smilga's original analysis for the finite volume partition function. method 0.99 0.86 0.07 asserted 1.00
s2 This is a further evidence that Ginsparg-Wilson fermions, even if breaking explicitly the chirality on the lattice in accordance to the Nielsen-Ninomiya theorem, mimic the main features of the continuum theory related to chiral symmetry. interpretation 1.00 0.29 0.18 asserted 0.65

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.68.

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  • references and citing sentences
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  • T body sentences
  • C citations
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We argue that lattice QCD with Ginsparg-Wilson fermions satisfies the Leutwyler-Smilga sum rules for the eigenvalues of the chiral Dirac operator. The result is obtained in the one flavor case, by rephrasing Leutwyler and Smilga's original analysis for the finite volume partition function. This is a further evidence that Ginsparg-Wilson fermions, even if breaking explicitly the chirality on the lattice in accordance to the Nielsen-Ninomiya theorem, mimic the main features of the continuum theory related to chiral symmetry.

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References
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1 arXiv paper cite this in 1 sentence

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it

Uses its method or tool 1 paper
  • All the eigenvalues $λ_lat$ of $D$, which lie on a circle with the radius of $ρ$ in a complex plain, are stereographically projected onto the imaginary axis via Möbius transformation [ref] , [equation] The spatial volumes are all fixed to $12^3$ and we adopt 5 different temporal lengths, $N_t=1/T$ = 4, 6, 8, 10, and 12.

    Low-lying Dirac eigenmodes and monopoles in 3+1D compact QED · Formalism · 1.00

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