Mathieu Moonshine in the elliptic genus of K3

Abstract

It has recently been conjectured that the elliptic genus of K3 can be written in terms of dimensions of Mathieu group M24 representations. Some further evidence for this idea was subsequently found by studying the twining genera that are obtained from the elliptic genus upon replacing dimensions of Mathieu group representations by their characters. In this paper we find explicit formulae for all (remaining) twining genera by making an educated guess for their general modular properties. This allows us to identify the decomposition of all expansion coefficients in terms of dimensions of M24-representations. For the first 500 coefficients we verify that the multiplicities with which these representations appear are indeed all non-negative integers. This represents very compelling evidence in favour of the conjecture.

arXiv comment23 pages; an error corrected, references updated

References in corpus (2)

• Mathieu twining characters for K3
• Product Representation of Dyon Partition Function in CHL Models

Cited by in corpus (46)

• State Operator Correspondence and Entanglement in AdS_2/CFT_1
• M-strings, Elliptic Genera and N=4 String Amplitudes
• Modular Constraints on Calabi-Yau Compactifications
• M String, Monopole String and Modular Forms
• Fricke S-duality in CHL models
• Mock Modular Mathieu Moonshine Modules
• A K3 sigma model with Z_2^8:M_{20} symmetry
• Mathieu Moonshine and N=2 String Compactifications
• The overarching finite symmetry group of Kummer surfaces in the Mathieu group M_24
• Unravelling Mathieu Moonshine
• Conformal Field Theories with Sporadic Group Symmetry
• On symmetries of N=(4,4) sigma models on T^4
• Moonshine, Superconformal Symmetry, and Quantum Error Correction
• No More Walls! A Tale of Modularity, Symmetry, and Wall Crossing for 1/4 BPS Dyons
• Lifting 1/4-BPS States on K3 and Mathieu Moonshine
• From Little String Free Energies Towards Modular Graph Functions
• A twist in the M24 moonshine story
• Moonshine in Fivebrane Spacetimes
• Self-Dual Vertex Operator Superalgebras and Superconformal Field Theory
• BPS Algebras, Genus Zero, and the Heterotic Monster
• Twining Genera of (0,4) Supersymmetric Sigma Models on K3
• Heterotic string on the CHL orbifold of K3
• Mathieu moonshine in four dimensional $\mathcal{N}=1$ theories
• Gauge Threshold Corrections for N = 2 Heterotic Local Models with Flux, and Mock Modular Forms
• Eta Products, BPS States and K3 Surfaces
• Comments on M${}_{24}$ representations and $C{Y}_3$ geometries
• Hodge-elliptic genera and how they govern K3 theories
• Enhanced Gauge Groups in N=4 Topological Amplitudes and Lorentzian Borcherds Algebras
• Snapshots of Conformal Field Theory
• Mathieu Moonshine and Symmetry Surfing
• N=2 Moonshine
• On Mathieu moonshine and Gromov-Witten invariants
• Refined Partition Functions for Open Superstrings with 4, 8 and 16 Supercharges
• Twisted elliptic genus for K3 and Borcherds product
• SU(2) channels the cancellation of K3 BPS states
• Ramanujan's influence on string theory, black holes and moonshine
• Not Doomed to Fail
• Calabi-Yau manifolds and sporadic groups
• Quasimodular moonshine and arithmetic connections
• Mathieu Moonshine and symmetries of K3 sigma models
• Vertex operator superalgebra/sigma model correspondences: The four-torus case
• Some comments on symmetric orbifolds of K3
• Lost Chapters in CHL Black Holes: Untwisted Quarter-BPS Dyons in the ${\mathbb{Z}}_2$ Model
• Mock Modularity Of Twisted Index In CHL Models
• Rényi entropy of single-character CFTs on the torus
• Tracking the symmetries of ${\mathbb{Z}}_3$-orbifold K3s within the Mathieu groups