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Mirror Symmetry and Supermanifolds

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Mina Aganagic, Cumrun Vafa

High Energy Physics - Theory · Submitted 19 Mar 2004

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

The authors' main claim We develop techniques for obtaining the mirror of Calabi-Yau supermanifolds as super-Landau-Ginzburg theories.

how it is stated · asserted 1.00 read the record →

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arXiv IDhep-th/0403192 (version 1)
Pith IDQ32KU3VJ, Pith's permanent record of this paper and its review
CitationCumrun Vafa, Mina Aganagic. "Mirror Symmetry and Supermanifolds." arXiv:hep-th/0403192 (2004). https://pith.science/paper/Q32KU3VJ
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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, 4,993 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.48 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.16 · compares with prior results 0.70 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We develop techniques for obtaining the mirror of Calabi-Yau supermanifolds as super-Landau-Ginzburg theories. In some cases the dual can be equivalent to a geometry. We apply this to some examples. In particular we show that the mirror of the twistorial Calabi-Yau CP^{3|4} becomes equivalent to a quadric in CP^{3|3} x CP^{3|3} as had been recently conjectured (in the limit where the K\"ahler parameter of CP^{3|4} t -> \pm \infty). Moreover, we show using these techniques that there is a non-trivial Z_2 symmetry for the K\"ahler parameter, t -> -t, which exchanges the opposite helicity states. As another class of examples, we show that the mirror of certain weighted projective (n+1|1) superspaces is equivalent to compact Calabi-Yau hypersurfaces in weighted projective n-space.

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 develop techniques for obtaining the mirror of Calabi-Yau supermanifolds as super-Landau-Ginzburg theories. contribution 0.95 0.96 0.37 asserted 1.00
s1 In some cases the dual can be equivalent to a geometry. result 0.88 0.46 0.06 hedged possibility 0.76
s2 We apply this to some examples. contribution 0.84 0.90 0.03 asserted 0.82
s3 In particular we show that the mirror of the twistorial Calabi-Yau CP^{3|4} becomes equivalent to a quadric in CP^{3|3} x CP^{3|3} as had been recently conjectured (in the limit where the K\"ahler parameter of CP^{3|4} t -> \pm \infty). result 0.98 0.87 0.36 asserted 1.00
s4 Moreover, we show using these techniques that there is a non-trivial Z_2 symmetry for the K\"ahler parameter, t -> -t, which exchanges the opposite helicity states. result 0.99 0.95 0.15 asserted 1.00
s5 As another class of examples, we show that the mirror of certain weighted projective (n+1|1) superspaces is equivalent to compact Calabi-Yau hypersurfaces in weighted projective n-space. result 0.88 0.95 0.11 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.73 · evidence from proof or derivation 1.00.

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  • arXiv listing abstract v1
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

We develop techniques for obtaining the mirror of Calabi-Yau supermanifolds as super-Landau-Ginzburg theories. In some cases the dual can be equivalent to a geometry. We apply this to some examples. In particular we show that the mirror of the twistorial Calabi-Yau CP^{3|4} becomes equivalent to a quadric in CP^{3|3} x CP^{3|3} as had been recently conjectured (in the limit where the K\"ahler parameter of CP^{3|4} t -> \pm \infty). Moreover, we show using these techniques that there is a non-trivial Z_2 symmetry for the K\"ahler parameter, t -> -t, which exchanges the opposite helicity states. As another class of examples, we show that the mirror of certain weighted projective (n+1|1) superspaces is equivalent to compact Calabi-Yau hypersurfaces in weighted projective n-space.

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References
How the literature uses it

3 arXiv papers cite this in 3 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

Cites it as background 3 papers
  • A foundational framework for the supergeometric extension of mirror symmetry was established by Aganagic and Vafa [ref] , who developed techniques for obtaining the mirrors of Calabi-Yau supermanifolds as super Landau-Ginzburg theories.

    Quantum Airy Structures and Matrix Models: a supercurrent approach · Introduction · 0.93

  • Supersymmetric sigma models on these spaces have been investigated by several authors (see e.g. [ref] ) after Witten had proposed the open topological B-model on as a candidate for a string theoretic description of N=4 super Yang-Mills theory [ref] .

    The Sigma Model on Complex Projective Superspaces · Introduction · 0.91

  • These include the supersymmetric sigma model on the so-called twistorial Calabi-Yau $ℂP^3|4$ that featured in Witten's work [ref] on twistor string theory (see e.g. [ref] ).

    N=2 Superconformal Symmetry in Super Coset Models · Introduction · 0.94

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