Gravitational couplings in N=2 string compactifications and Mathieu Moonshine

A bstract We evaluate the low energy gravitational couplings, F g in the heterotic E 8 × E 8 string theory compactified on orbifolds of K 3 × T 2 by g ′ which acts as a ℤ N automorphism on K 3 together with a 1 /N shift along T 2 . The orbifold g ′ corresponds to the conjugacy classes of the Mathieu...

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Bibliographic Details
Published in:The journal of high energy physics Vol. 2018; no. 5; pp. 1 - 55
Main Authors: Chattopadhyaya, Aradhita, David, Justin R.
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 31.05.2018
Springer Nature B.V
Subjects:
Automorphisms
Classical and Quantum Gravitation
Couplings
Elementary Particles
Gravitation theory
High energy physics
Integers
Invariants
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
String Theory
Discrete Symmetries
Topological Strings
Superstrings and Heterotic Strings
ISSN:1029-8479
Online Access:Get full text
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Summary:A bstract We evaluate the low energy gravitational couplings, F g in the heterotic E 8 × E 8 string theory compactified on orbifolds of K 3 × T 2 by g ′ which acts as a ℤ N automorphism on K 3 together with a 1 /N shift along T 2 . The orbifold g ′ corresponds to the conjugacy classes of the Mathieu group M 24 . The holomorphic piece of F g is given in terms of a polylogarithm with index 3−2 g 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.
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ISSN:1029-8479
DOI:10.1007/JHEP05(2018)211