Lifting 14 -BPS States on K3 and Mathieu Moonshine

Christoph A. Keller; Ida G. Zadeh

doi:10.1007/s00220-020-03721-4

Lifting 14 -BPS States on K3 and Mathieu Moonshine

Christoph A. Keller, Ida G. Zadeh

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

16 Scopus citations

Abstract

The elliptic genus of K3 is an index for the 14-BPS states of its σ-model. At the torus orbifold point there is an accidental degeneracy of such states. We blow up the orbifold fixed points using conformal perturbation theory, and find that this fully lifts the accidental degeneracy of the 14-BPS states with h= 1. At a generic point near the Kummer surface the elliptic genus thus measures not just their index, but counts the actual number of these BPS states. We comment on the implication of this for symmetry surfing and Mathieu moonshine.

Original language	English (US)
Pages (from-to)	225-257
Number of pages	33
Journal	Communications in Mathematical Physics
Volume	377
Issue number	1
DOIs	https://doi.org/10.1007/s00220-020-03721-4
State	Published - Jul 1 2020
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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abstract = "The elliptic genus of K3 is an index for the 14-BPS states of its σ-model. At the torus orbifold point there is an accidental degeneracy of such states. We blow up the orbifold fixed points using conformal perturbation theory, and find that this fully lifts the accidental degeneracy of the 14-BPS states with h= 1. At a generic point near the Kummer surface the elliptic genus thus measures not just their index, but counts the actual number of these BPS states. We comment on the implication of this for symmetry surfing and Mathieu moonshine.",

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N2 - The elliptic genus of K3 is an index for the 14-BPS states of its σ-model. At the torus orbifold point there is an accidental degeneracy of such states. We blow up the orbifold fixed points using conformal perturbation theory, and find that this fully lifts the accidental degeneracy of the 14-BPS states with h= 1. At a generic point near the Kummer surface the elliptic genus thus measures not just their index, but counts the actual number of these BPS states. We comment on the implication of this for symmetry surfing and Mathieu moonshine.

AB - The elliptic genus of K3 is an index for the 14-BPS states of its σ-model. At the torus orbifold point there is an accidental degeneracy of such states. We blow up the orbifold fixed points using conformal perturbation theory, and find that this fully lifts the accidental degeneracy of the 14-BPS states with h= 1. At a generic point near the Kummer surface the elliptic genus thus measures not just their index, but counts the actual number of these BPS states. We comment on the implication of this for symmetry surfing and Mathieu moonshine.

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Lifting 14 -BPS States on K3 and Mathieu Moonshine

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