Mathieu Moonshine and symmetry surfing

Matthias R. Gaberdiel; Christoph A. Keller; Hynek Paul

doi:10.1088/1751-8121/aa915f

Mathieu Moonshine and symmetry surfing

Matthias R. Gaberdiel
, Christoph A. Keller
, Hynek Paul

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

Mathieu Moonshine, the observation that the Fourier coefficients of the elliptic genus on K3 can be interpreted as dimensions of representations of the Mathieu group M₂₄, has been proven abstractly, but a conceptual understanding in terms of a representation of the Mathieu group on the BPS states, is missing. Some time ago, Taormina and Wendland showed that such an action can be naturally defined on the lowest non-trivial BPS states, using the idea of symmetry surfing, i.e. by combining the symmetries of different K3 sigma models. In this paper we find non-trivial evidence that this construction can be generalized to all BPS states.

Original language	English (US)
Article number	474002
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	50
Issue number	47
DOIs	https://doi.org/10.1088/1751-8121/aa915f
State	Published - Nov 1 2017
Externally published	Yes

Keywords

Mathieu Moonshine
modular forms
vertex operator algebras

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Statistics and Probability
Modeling and Simulation
Mathematical Physics
General Physics and Astronomy

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10.1088/1751-8121/aa915f

Cite this

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title = "Mathieu Moonshine and symmetry surfing",

abstract = "Mathieu Moonshine, the observation that the Fourier coefficients of the elliptic genus on K3 can be interpreted as dimensions of representations of the Mathieu group M24, has been proven abstractly, but a conceptual understanding in terms of a representation of the Mathieu group on the BPS states, is missing. Some time ago, Taormina and Wendland showed that such an action can be naturally defined on the lowest non-trivial BPS states, using the idea of symmetry surfing, i.e. by combining the symmetries of different K3 sigma models. In this paper we find non-trivial evidence that this construction can be generalized to all BPS states.",

keywords = "Mathieu Moonshine, modular forms, vertex operator algebras",

author = "Gaberdiel, \{Matthias R.\} and Keller, \{Christoph A.\} and Hynek Paul",

note = "Funding Information: This paper is based on the Master thesis of one of us (HP). We thank Jeff Harvey and Greg Moore for initial collaboration on this project. It is a pleasure to thank Simeon Hellerman, Geoff Mason, Anne Taormina, Roberto Volpato, Katrin Wendland for helpful discussions. CAK thanks the Harvard University High Energy Theory Group for hospitality. CAK is supported by the Swiss National Science Foundation through the NCCR SwissMAP. The research of MRG is also supported partly by the NCCR SwissMAP, funded by the Swiss National Science Foundation.",

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doi = "10.1088/1751-8121/aa915f",

language = "English (US)",

volume = "50",

journal = "Journal of Physics A: Mathematical and Theoretical",

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AU - Gaberdiel, Matthias R.

AU - Keller, Christoph A.

AU - Paul, Hynek

N1 - Funding Information: This paper is based on the Master thesis of one of us (HP). We thank Jeff Harvey and Greg Moore for initial collaboration on this project. It is a pleasure to thank Simeon Hellerman, Geoff Mason, Anne Taormina, Roberto Volpato, Katrin Wendland for helpful discussions. CAK thanks the Harvard University High Energy Theory Group for hospitality. CAK is supported by the Swiss National Science Foundation through the NCCR SwissMAP. The research of MRG is also supported partly by the NCCR SwissMAP, funded by the Swiss National Science Foundation.

PY - 2017/11/1

Y1 - 2017/11/1

N2 - Mathieu Moonshine, the observation that the Fourier coefficients of the elliptic genus on K3 can be interpreted as dimensions of representations of the Mathieu group M24, has been proven abstractly, but a conceptual understanding in terms of a representation of the Mathieu group on the BPS states, is missing. Some time ago, Taormina and Wendland showed that such an action can be naturally defined on the lowest non-trivial BPS states, using the idea of symmetry surfing, i.e. by combining the symmetries of different K3 sigma models. In this paper we find non-trivial evidence that this construction can be generalized to all BPS states.

AB - Mathieu Moonshine, the observation that the Fourier coefficients of the elliptic genus on K3 can be interpreted as dimensions of representations of the Mathieu group M24, has been proven abstractly, but a conceptual understanding in terms of a representation of the Mathieu group on the BPS states, is missing. Some time ago, Taormina and Wendland showed that such an action can be naturally defined on the lowest non-trivial BPS states, using the idea of symmetry surfing, i.e. by combining the symmetries of different K3 sigma models. In this paper we find non-trivial evidence that this construction can be generalized to all BPS states.

KW - Mathieu Moonshine

KW - modular forms

KW - vertex operator algebras

UR - https://www.scopus.com/pages/publications/85034221595

UR - https://www.scopus.com/pages/publications/85034221595#tab=citedBy

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DO - 10.1088/1751-8121/aa915f

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JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

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M1 - 474002

ER -

Mathieu Moonshine and symmetry surfing

Abstract

Keywords

ASJC Scopus subject areas

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