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Random loops and conformal field theory

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Benjamin Doyon

Mathematical Physics · Submitted 11 Feb 2014

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

The authors' main claim This is a review of results obtained by the author concerning the relation between conformally invariant random loops and conformal field theory.

how it is stated · asserted 0.96 read the record →

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arXiv ID1402.2432 (version 2)
Pith IDNN34WZOK, Pith's permanent record of this paper and its review
CitationBenjamin Doyon. "Random loops and conformal field theory." arXiv:1402.2432 (2014). https://pith.science/paper/NN34WZOK
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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.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,273 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.07 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.10 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

This is a review of results obtained by the author concerning the relation between conformally invariant random loops and conformal field theory. This review also attempts to provide a physical context in which to interpret these results by making connections with aspects of the nucleation theory of phase transitions and with general properties of criticality.

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 This is a review of results obtained by the author concerning the relation between conformally invariant random loops and conformal field theory. contribution 0.91 0.70 0.15 asserted 0.96
s1 This review also attempts to provide a physical context in which to interpret these results by making connections with aspects of the nucleation theory of phase transitions and with general properties of criticality. interpretation 0.51 0.39 0.09 asserted 0.49

What kind of paper the classifier reports this is: review 1.00 · evidence from literature 0.80.

What was examined, and what was not

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  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • 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

This is a review of results obtained by the author concerning the relation between conformally invariant random loops and conformal field theory. This review also attempts to provide a physical context in which to interpret these results by making connections with aspects of the nucleation theory of phase transitions and with general properties of criticality.

Human review

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How the literature uses it

What this paper does with the arXiv papers it cites

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

What it cites · 60 sentences without a confident label

Builds on 2 papers
  • Relation [ref] was also generalized to multiply connected domains in [ref] , where the only change is in the definition of the relative partition function: let $U_i, i=1,…,n$ be Jordan domains with pairwise disjoint complements, let $U = U_1∩U_2∩⋯∩U_n$, $u_i = U_i$ and $u =U$, and let $v⊂U$ be a Jordain curve, then Z(u,v) := 𝔼[∏_i (u_i)]_ 𝔼[∏_i (u_i)]_V, v=V, u⊂V.

    Hypotrochoids in conformal restriction systems and Virasoro descendants · Extended conformal Ward identities · 0.83

  • This construction was extended in [ref] to a construction of the full Virasoro vertex operator algebra [ref] , providing a reinterpretation of Huang's geometric vertex operator algebra [ref] that is adapted to the mathematics of statistical field theory.

    Higher conformal variations and the Virasoro vertex operator algebra · Conformal geometry · 0.95

Uses the method or tool of 4 papers
  • The mathematical tools used are studied in [ref] , and are adaptations to the present context of concepts of geometric vertex operator algebras [ref] , connecting measure-theoretic, analytic and algebraic descriptions of CFT.

    Calculus on manifolds of conformal maps and CFT · Introduction · 0.93

  • The mathematical tools used are studied in [ref] , and are adaptations to the present context of concepts of geometric vertex operator algebras [ref] , connecting measure-theoretic, analytic and algebraic descriptions of CFT.

    Higher conformal variations and the Virasoro vertex operator algebra · Introduction · 0.93

  • The mathematical tools used are studied in [ref] , and are adaptations to the present context of concepts of geometric vertex operator algebras [ref] , connecting measure-theoretic, analytic and algebraic descriptions of CFT.

    A functional-analytic theory of vertex (operator) algebras, II · Introduction · 0.93

Cites as background 13 papers
  • CLEs are families of conformally invariant measures for random loops on domains of the plane [ref] , which emerged as generalizations of Schramm Loewner evolutions (SLEs) [ref] .

    A Guide to Stochastic Loewner Evolution and its Applications · Introduction · 0.97

  • CLEs are families of conformally invariant measures for random loops on domains of the plane [ref] , which emerged as generalizations of Schramm Loewner evolutions (SLEs) [ref] .

    math.PR/0303354 · Introduction · 0.97

  • CLEs are families of conformally invariant measures for random loops on domains of the plane [ref] , which emerged as generalizations of Schramm Loewner evolutions (SLEs) [ref] .

    math.PR/0609167 · Introduction · 0.97

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