Gravitational couplings in {\cal N}=2 string compactifications and Mathieu Moonshine

Chattopadhyaya, Aradhita ; David, Justin R. (2018) Gravitational couplings in {\cal N}=2 string compactifications and Mathieu Moonshine Journal of High Energy Physics, 2018 (5). ISSN 1029-8479

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We evaluate the low energy gravitational couplings, Fg in the heterotic E8 ×E8 string theory compactified on orbifolds of K3 × T 2 by g′ which acts as a ℤN automorphism on K3 together with a 1/N shift along T 2. The orbifold g′ corresponds to the conjugacy classes of the Mathieu group M24. The holomorphic piece of Fg is given in terms of a polylogarithm with index 3−2g and predicts the Gopakumar-Vafa invariants in the corresponding dual type II Calabi-Yau compactifications. We show that low lying Gopakumar-Vafa invariants for each of these compactifications including the twisted sectors are integers. We observe that the conifold singularity for all these compactifications occurs only when states in the twisted sectors become massless and the strength of the singularity is determined by the genus zero Gopakumar-Vafa invariant at this point in the moduli space.

Item Type:Article
Source:Copyright of this article belongs to Springer Nature Switzerland AG.
Keywords:Superstrings and Heterotic Strings; Discrete Symmetries; Topological Strings.
ID Code:116993
Deposited On:14 Apr 2021 08:12
Last Modified:14 Apr 2021 08:12

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