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Platonic Sphalerons

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B. Kleihaus, J. Kunz, K. Myklevoll

High Energy Physics - Theory · Submitted 31 Oct 2003

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

The authors' main claim We construct sphaleron solutions in Weinberg-Salam theory, which possess only discrete symmetries.

how it is stated · asserted 1.00 read the record →

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arXiv IDhep-th/0310300 (version 1)
Pith IDVUTIWQXC, Pith's permanent record of this paper and its review
CitationB. Kleihaus, J. Kunz, K. Myklevoll. "Platonic Sphalerons." arXiv:hep-th/0310300 (2003). https://pith.science/paper/VUTIWQXC
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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.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,531 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.16 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.88 · compares with prior results 0.07 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We construct sphaleron solutions in Weinberg-Salam theory, which possess only discrete symmetries. Related to rational maps of degree N, these sphalerons carry baryon number Q_B=N/2. The energy density of these sphalerons reflects their discrete symmetries. We present an N=3 sphaleron with tetrahedral energy density, an N=4 sphaleron with cubic energy density, and an N=5 sphaleron with octahedral energy density.

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 construct sphaleron solutions in Weinberg-Salam theory, which possess only discrete symmetries. contribution 0.99 0.95 0.42 asserted 1.00
s1 Related to rational maps of degree N, these sphalerons carry baryon number Q_B=N/2. result 0.90 0.68 0.23 asserted 1.00
s2 The energy density of these sphalerons reflects their discrete symmetries. result 0.67 0.70 0.11 asserted 1.00
s3 We present an N=3 sphaleron with tetrahedral energy density, an N=4 sphaleron with cubic energy density, and an N=5 sphaleron with octahedral energy density. result 0.51 0.92 0.33 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.78.

What was examined, and what was not

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  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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 construct sphaleron solutions in Weinberg-Salam theory, which possess only discrete symmetries. Related to rational maps of degree N, these sphalerons carry baryon number Q_B=N/2. The energy density of these sphalerons reflects their discrete symmetries. We present an N=3 sphaleron with tetrahedral energy density, an N=4 sphaleron with cubic energy density, and an N=5 sphaleron with octahedral energy density.

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References
How the literature uses it

4 arXiv papers cite this in 4 sentences

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 · 3 sentences without a confident label

Cites it as background 1 paper
  • Although they were first discovered in the SU(2) [ref] and U(1)$×$SU(2) Higgs models [ref] [ref] [ref] (where Nambu's embedded vortices [ref] were also retroactively recognized as sphalerons [ref] [ref] ), they have since turned up elsewhere too, from QCD [ref] to Einstein-Yang-Mills theory (YM coupled to gravity) [ref] [ref] , showing that the primary role of $Φ$ in enabling their emergence is to provide a finite energy scale for the barriers.

    Unitary gauge considered harmful · Instantons and sphalerons · 0.82

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