Mathieu Moonshine and symmetries of K3 sigma models

Roberto Volpato

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Mathieu Moonshine and symmetries of K3 sigma models

Roberto Volpato

High Energy Physics - Theory · Submitted 30 Jan 2012

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim However, all possible symmetry groups of K3 models have been recently classified and none of them contains M24.

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.38 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.32 · mentions code or data availability 0.02.

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A recent observation by Eguchi, Ooguri and Tachikawa (EOT) suggests a relationship between the largest Mathieu group M24 and the elliptic genus of K3. This correspondence would be naturally explained by the existence of a non-linear sigma-model on K3 with the Mathieu group as its group of symmetries. However, all possible symmetry groups of K3 models have been recently classified and none of them contains M24. We review the evidence in favour of the EOT conjecture and discuss the open problems in its physical interpretation.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	A recent observation by Eguchi, Ooguri and Tachikawa (EOT) suggests a relationship between the largest Mathieu group M24 and the elliptic genus of K3.	background 1.00	0.03	0.05	hedged possibility 1.00
s1	This correspondence would be naturally explained by the existence of a non-linear sigma-model on K3 with the Mathieu group as its group of symmetries.	background 0.58	0.05	0.08	hedged possibility 0.77
s2	However, all possible symmetry groups of K3 models have been recently classified and none of them contains M24.	background 0.81	0.09	0.42	asserted 1.00
s3	We review the evidence in favour of the EOT conjecture and discuss the open problems in its physical interpretation.	contribution 0.97	0.68	0.09	unclear 0.68

What kind of paper the classifier reports this is: review 0.99 · evidence from literature 0.86.

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The paper

Original abstract

A recent observation by Eguchi, Ooguri and Tachikawa (EOT) suggests a relationship between the largest Mathieu group M24 and the elliptic genus of K3. This correspondence would be naturally explained by the existence of a non-linear sigma-model on K3 with the Mathieu group as its group of symmetries. However, all possible symmetry groups of K3 models have been recently classified and none of them contains M24. We review the evidence in favour of the EOT conjecture and discuss the open problems in its physical interpretation.

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2 arXiv papers cite this in 3 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it

Cites it as background 2 papers

Mathieu moonshine [ref] and its generalized version [ref] pertain to the association of a class of weak Jacobi forms $ϕ_g,h(τ, z)$, called twisted twining genera, to each commuting pair of elements $(g,h)$ in $M_24$.

Second Quantized Mathieu Moonshine · Introduction and Summary · 0.99
See also [ref] for reviews and [ref] for related discussions.

Umbral Moonshine · Lambency Two · 0.97

What it cites · 24 sentences without a confident label

Uses the method or tool of 1 paper

The construction in [ref] provides a systematic way to describe the full group $G$ of symmetries by studying the automorphisms of the D-brane lattice.

Symmetries of K3 sigma models · Symmetries of K3 $σ$-models · 0.97

Cites as support 1 paper

For example, in [ref] it is shown that only the twining genera from $_24$ elements satisfy a certain genus 0 property, analogous to the McKay-Thompson series in the Monster Moonshine.

On Rademacher Sums, the Largest Mathieu Group, and the Holographic Modularity of Moonshine · Discussion · 0.98

Cites as background 2 papers

The proof is based on general properties of non-linear $σ$-models of K3 (see [ref] for a review).

K3 Surfaces and String Duality · Symmetries of K3 $σ$-models · 0.93
The proof is based on general properties of non-linear $σ$-models of K3 (see [ref] for a review).

A Hiker's Guide to K3 - Aspects of N=(4,4) Superconformal Field Theory with central charge c=6 · Symmetries of K3 $σ$-models · 0.93

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