The Moonshine Anomaly View Full Text


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Article Info

DATE

2019-02

AUTHORS

Theo Johnson-Freyd

ABSTRACT

The anomaly for the Monster group M acting on its natural (aka moonshine) representation V♮ is a particular cohomology class ω♮∈H3(M,U(1)) that arises as a conformal field theoretic generalization of the second Chern class of a representation. This paper shows that ω♮ has order exactly 24 and is not a Chern class. In order to perform this computation, this paper introduces a finite-group version of T-duality, which is used to relate ω♮ to the anomaly for the Leech lattice CFT. More... »

PAGES

943-970

References to SciGraph publications

  • 2004-11. Topological Sectors and a Dichotomy in Conformal Field Theory in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1998-04. Framed Vertex Operator Algebras, Codes and the Moonshine Module in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2002-08. Modular Categories and Orbifold Models in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1993-10. Chern-Simons theory with finite gauge group in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2017-08. Conformal Nets II: Conformal Blocks in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1990-04. Topological gauge theories and group cohomology in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1989-09. The operator algebra of orbifold models in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1996-11. The conformal spin and statistics theorem in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1992-05. Monstrous Moonshine from orbifolds in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2017. Monoidal Categories and Topological Field Theory in NONE
  • 1984-03. Chern-Klassen von ganzzahligen und rationalen Darstellungen diskreter Gruppen in MATHEMATISCHE ZEITSCHRIFT
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    http://scigraph.springernature.com/pub.10.1007/s00220-019-03300-2

    DOI

    http://dx.doi.org/10.1007/s00220-019-03300-2

    DIMENSIONS

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    51 schema:description The anomaly for the Monster group M acting on its natural (aka moonshine) representation V♮ is a particular cohomology class ω♮∈H3(M,U(1)) that arises as a conformal field theoretic generalization of the second Chern class of a representation. This paper shows that ω♮ has order exactly 24 and is not a Chern class. In order to perform this computation, this paper introduces a finite-group version of T-duality, which is used to relate ω♮ to the anomaly for the Leech lattice CFT.
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