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Nonplanar Integrability and Parity in ABJ Theory

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Badr Awad Elseid Mohammed

High Energy Physics - Theory · Submitted 30 Jul 2012

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

The authors' main claim Our analysis shows that (M-N) is related to the holonomy in the string theory, confirming one of the main features of the theory and its string dual.

how it is stated · asserted 1.00 read the record →

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arXiv ID1207.6948 (version 4)
Pith IDATBXJWTM, Pith's permanent record of this paper and its review
CitationBadr Awad Elseid Mohammed. "Nonplanar Integrability and Parity in ABJ Theory." arXiv:1207.6948 (2012). https://pith.science/paper/ATBXJWTM
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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, 5,507 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.24 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.50 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; .

In this article we study the action of the non-planar two-loop dilatation operator in an SU(2)*SU(2) sub-sector of the ABJ Chern-Simons-matter theory. The gauge invariant operators we consider are the restricted Schur polynomials. As in ABJM theory, there is a limit in which the spectrum reduces to a set of decoupled harmonic oscillators, indicating integrability in the large M and N double limit of the theory. We then consider parity transformations on the gauge invariant operators. In this case the non-planar anomalous dimensions break parity invariance. Our analysis shows that (M-N) is related to the holonomy in the string theory, confirming one of the main features of the theory and its string dual. Furthermore, in the limit where ABJ theory reduces to ABJM theory, parity invariance is restored.

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 In this article we study the action of the non-planar two-loop dilatation operator in an SU(2)*SU(2) sub-sector of the ABJ Chern-Simons-matter theory. contribution 0.99 0.87 0.04 asserted 0.74
s1 The gauge invariant operators we consider are the restricted Schur polynomials. method 0.54 0.36 0.02 asserted 1.00
s2 As in ABJM theory, there is a limit in which the spectrum reduces to a set of decoupled harmonic oscillators, indicating integrability in the large M and N double limit of the theory. result 0.92 0.56 0.19 hedged possibility 0.71
s3 We then consider parity transformations on the gauge invariant operators. contribution 0.96 0.81 0.03 asserted 0.63
s4 In this case the non-planar anomalous dimensions break parity invariance. result 1.00 0.81 0.24 asserted 1.00
s5 Our analysis shows that (M-N) is related to the holonomy in the string theory, confirming one of the main features of the theory and its string dual. result 0.62 0.85 0.40 asserted 1.00
s6 Furthermore, in the limit where ABJ theory reduces to ABJM theory, parity invariance is restored. result 0.98 0.78 0.15 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.98.

What was examined, and what was not

sources read
  • arXiv listing abstract v4
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

In this article we study the action of the non-planar two-loop dilatation operator in an SU(2)*SU(2) sub-sector of the ABJ Chern-Simons-matter theory. The gauge invariant operators we consider are the restricted Schur polynomials. As in ABJM theory, there is a limit in which the spectrum reduces to a set of decoupled harmonic oscillators, indicating integrability in the large M and N double limit of the theory. We then consider parity transformations on the gauge invariant operators. In this case the non-planar anomalous dimensions break parity invariance. Our analysis shows that (M-N) is related to the holonomy in the string theory, confirming one of the main features of the theory and its string dual. Furthermore, in the limit where ABJ theory reduces to ABJM theory, parity invariance is restored.

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How the literature uses it

5 arXiv papers cite this in 5 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 2 papers
  • For quiver gauge theories, there are two distinct approaches that have been developed to study the finite $N$ physics [ref] [For earlier work, focusing on essentially single matrix dynamics, see [ref] ].

    Finite N Quiver Gauge Theory · Summary and Conclusions · 0.97

  • The studies were extended beyond $=4$ SYM to gauge theories such as ABJM [ref] and the conifold [ref] .

    Quivers, Words and Fundamentals · Introduction · 0.80

What it cites · 35 sentences without a confident label

Compares with 6 papers
  • The computation of [ref] gives [equation] [equation] [equation] [equation] where [equation] The combination $Ô_j,j^3(b_0,b_1)$ in [ref] differs from the ones obtained in the case of $N=4$ SYM theory and ABJM theory [ref] , since it depends on both $M$ and $N$.

    Beyond the Planar Limit in ABJM · Spectrum of Anomalous Dimensions · 0.91

  • The computation of [ref] gives [equation] [equation] [equation] [equation] where [equation] The combination $Ô_j,j^3(b_0,b_1)$ in [ref] differs from the ones obtained in the case of $N=4$ SYM theory and ABJM theory [ref] , since it depends on both $M$ and $N$.

    Nonplanar Integrability · Spectrum of Anomalous Dimensions · 0.91

  • In contrast to this, the spin chains technique for ABJM which is relevant for expansion about the planar limit of the theory did not find any sign of non-planar integrability [ref] .

    Non-planar ABJM Theory and Integrability · Introduction · 0.88

Cites as background 1 paper

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