Notes on the K3 Surface and the Mathieu group M_24

Abstract

We point out that the elliptic genus of the K3 surface has a natural decomposition in terms of dimensions of irreducible representations of the largest Mathieu group M_24. The reason is yet a mystery.

10 pages. v2: published version

References in corpus (6)

• Three-Dimensional Gravity Revisited
• Mock Theta Functions
• Mathieu twining characters for K3
• K3 Surfaces, N=4 Dyons, and the Mathieu Group M24
• N=4 Superconformal Algebra and the Entropy of HyperKahler Manifolds
• Superconformal Algebras and Mock Theta Functions 2. Rademacher Expansion for K3 Surface

Cited by in corpus (148)

• Quantum Black Holes, Wall Crossing, and Mock Modular Forms
• Notes on generalized global symmetries in QFT
• Note on Twisted Elliptic Genus of K3 Surface
• Diagrammatics for Bose condensation in anyon theories
• Mathieu twining characters for K3
• State Operator Correspondence and Entanglement in AdS_2/CFT_1
• Eisenstein series and automorphic representations
• M-strings, Elliptic Genera and N=4 String Amplitudes
• Modular Constraints on Calabi-Yau Compactifications
• Moulting Black Holes
• Gravitational Positive Energy Theorems from Information Inequalities
• Narain to Narnia
• BKM Lie superalgebras from counting twisted CHL dyons
• Mock Modular Mathieu Moonshine Modules
• Fricke S-duality in CHL models
• The 290 fixed-point sublattices of the Leech lattice
• Holomorphic projections and Ramanujan's mock theta functions
• A K3 sigma model with Z_2^8:M_{20} symmetry
• Lifting 1/4-BPS States in $Ad{S}_3\times S^3\times T^4$
• Mathieu Moonshine and N=2 String Compactifications
• The overarching finite symmetry group of Kummer surfaces in the Mathieu group M_24
• Narain CFTs and error-correcting codes on finite fields
• Unravelling Mathieu Moonshine
• Conformal Field Theories with Sporadic Group Symmetry
• On symmetries of N=(4,4) sigma models on T^4
• Umbral Moonshine and the Niemeier Lattices
• Moonshine, Superconformal Symmetry, and Quantum Error Correction
• Generalised Mathieu Moonshine
• 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
• A Refined Count of BPS States in the D1/D5 System
• A twist in the M24 moonshine story
• Self-Dual Vertex Operator Superalgebras and Superconformal Field Theory
• Moonshine in Fivebrane Spacetimes
• BKM Lie superalgebras from counting twisted CHL dyons -- II
• A proof of the Thompson Moonshine Conjecture
• On a completed generating function of locally harmonic Maass forms
• Topological modularity of Supermoonshine
• The symmetries of the tetrahedral Kummer surface in the Mathieu group M_24
• Brewing moonshine for Mathieu
• Elliptic genera and real Jacobi forms
• BPS Algebras, Genus Zero, and the Heterotic Monster
• Fusion rules for the logarithmic $N=1$ superconformal minimal models I: the Neveu-Schwarz sector
• Clifford algebra is the natural framework for root systems and Coxeter groups. Group theory: Coxeter, conformal and modular groups
• Super Vertex Algebras, Meromorphic Jacobi Forms and Umbral Moonshine
• K3 String Theory, Lattices and Moonshine
• BPS Saturated String Amplitudes: K3 Elliptic Genus and Igusa Cusp Form
• Twining Genera of (0,4) Supersymmetric Sigma Models on K3
• Conway Subgroup Symmetric Compactifications Of Heterotic String
• APS $\eta$-invariant, path integrals, and mock modularity
• Heterotic string on the CHL orbifold of K3
• Generalised Umbral Moonshine
• Sporadic and Exceptional
• Exceptional Algebra and Sporadic Groups at c=12
• The Hodge-elliptic genus, spinning BPS states, and black holes
• Monster Anatomy
• $N=4$ superconformal algebras and diagonal cosets
• Non-geometric Calabi-Yau compactifications and fractional mirror symmetry
• Eta Products, BPS States and K3 Surfaces
• The Umbral Moonshine Module for the Unique Unimodular Niemeier Root System
• Gauge Threshold Corrections for N = 2 Heterotic Local Models with Flux, and Mock Modular Forms
• Mathieu moonshine in four dimensional $\mathcal{N}=1$ theories
• Dyon degeneracies from Mathieu moonshine
• Snapshots of Conformal Field Theory
• Proof of the Umbral Moonshine Conjecture
• Second Quantized Mathieu Moonshine
• A Borcherds-Kac-Moody superalgebra with Conway symmetry
• Mathieu Moonshine and Orbifold K3s
• Hodge-elliptic genera and how they govern K3 theories
• $a\times b=c$ in $2+1$D TQFT
• Umbral Moonshine and K3 Surfaces
• Comments on M${}_{24}$ representations and $C{Y}_3$ geometries
• Heterotic sigma models on $T^8$ and the Borcherds automorphic form ${\Phi }_{12}$
• 3D String Theory and Umbral Moonshine
• Dressed elliptic genus of heterotic compactifications with torsion and general bundles
• Powers of Jacobi triple product, Cohen's numbers and the Ramanujan $\Delta$-function
• ADE Double Scaled Little String Theories, Mock Modular Forms and Umbral Moonshine
• Gravitational couplings in $\mathcal{N}=2$ string compactifications and Mathieu Moonshine
• N=2 Moonshine
• Automorphisms and Periods of Cubic Fourfolds
• Supersingular Elliptic Curves and Moonshine
• Mathieu Moonshine and Symmetry Surfing
• Elementary introduction to Moonshine
• Wall-crossing holomorphic anomaly and mock modularity of multiple M5-branes
• Introduction to Sporadic Groups
• Enriques moonshine
• Introduction to Sporadic Groups for physicists
• Squashed toric sigma models and mock modular forms
• Symmetries of K3 sigma models
• Mocking the u-plane integral
• BKM Lie superalgebra for the Z_5 orbifolded CHL string
• Three-Charge Black Holes and Quarter BPS States in Little String Theory
• Extremal chiral $\mathcal{N}=4$ SCFT with $c=24$
• Geodesics on Calabi-Yau manifolds and winding states in nonlinear sigma models
• Kazama-Suzuki coset construction and its inverse
• The McKay-Thompson series of Mathieu Moonshine modulo two
• The Eichler cohomology theorem for Jacobi forms
• On Rational Points in CFT Moduli Spaces
• Harmonic Maass-Jacobi forms with singularities and a theta-like decomposition
• On Mathieu moonshine and Gromov-Witten invariants
• Symmetries of the refined D1/D5 BPS spectrum
• Twisted elliptic genus for K3 and Borcherds product
• Attractive Strings and Five-Branes, Skew-Holomorphic Jacobi Forms and Moonshine
• Recent advances and open questions on the susy structure of the chiral de Rham Complex
• From the Trinity $(A_3,B_3,H_3)$ to an ADE correspondence
• Positivity of discrete information for CHL black holes
• Duality in N=4 Liouville Theory and Moonshine Phenomena
• Two moonshines for $L_2(11)$ but none for $M_{12}$
• On the elliptic genera of manifolds of Spin(7) holonomy
• Quasimodular moonshine and arithmetic connections
• Conway Subgroup Symmetric Compactifications Redux
• Heterotic strings on $(K3\times T^2)/{\mathbb{Z}}_3$ and their dual Calabi-Yau threefolds
• Ramanujan's influence on string theory, black holes and moonshine
• SU(2) channels the cancellation of K3 BPS states
• Calabi-Yau manifolds and sporadic groups
• Not Doomed to Fail
• A 3D spinorial view of 4D exceptional phenomena
• Mathieu Moonshine and symmetries of K3 sigma models
• BPS Spectra, Barcodes and Walls
• Quarter-BPS states in orbifold sigma models with ADE singularities
• Umbral Moonshine and String Duality
• A short introduction to Monstrous Moonshine
• Invariant subalgebras of the small $\mathcal{N}=4$ superconformal algebra
• Vertex operator superalgebra/sigma model correspondences: The four-torus case
• Mathieu Moonshine and Siegel Modular Forms
• Gravitational couplings in $\mathcal{N}=2$ heterotic compactifications with Wilson lines
• Monstrous entanglement
• Modular Transformations of Ramanujan's Tenth Order Mock Theta Functions
• N=(4,4) Vector Multiplets on Curved Two-Manifolds
• U-Duality and the Leech Lattice
• Monstrous M-theory
• A non-commuting twist in the partition function
• Non-invertible defects from the Conway SCFT to K3 sigma models I: general results
• TASI Lectures on Moonshine
• Lost Chapters in CHL Black Holes: Untwisted Quarter-BPS Dyons in the ${\mathbb{Z}}_2$ Model
• Some comments on symmetric orbifolds of K3
• Non-Compact SCFT and Mock Modular Forms
• Kohnen's limit process for real-analytic Siegel modular forms
• Flavor Moonshine
• Topological Mathieu Moonshine
• The Monster, the Baby Monster and Traces of Singular Moduli
• Cohomological relation between Jacobi forms and skew-holomorphic Jacobi forms
• Tracking the symmetries of ${\mathbb{Z}}_3$-orbifold K3s within the Mathieu groups
• Mock Modularity Of Twisted Index In CHL Models
• Decompositions of index one Jacobi forms into $N=4$ characters and formulas for mock modular forms
• Professor Nambu, String Theory and Moonshine Phenomenon
• Young supertableaux and the large $\mathcal{N}=4$ superconformal algebra
• Algebraic surfaces, Four-folds and Moonshine