Unravelling Mathieu Moonshine
Reads0
Chats0
TLDR
In this article, the Mathieu group, M 24, acts on this module by recovering the Siegel modular forms that count twisted dyons as a trace over this module, which is done by recovering Borcherds product formulae for these modular forms using the M 24 action.About:
This article is published in Nuclear Physics.The article was published on 2012-11-21 and is currently open access. It has received 37 citations till now. The article focuses on the topics: Siegel modular form & Modular curve.read more
Citations
More filters
Journal ArticleDOI
Much ado about Mathieu
TL;DR: In this article, the integrality of multiplicities is proved using a small generalisation of Sturm's Theorem, while positivity involves a modification of a method of Hooley, for finding an effective bound on a family of Selberg-Kloosterman zeta functions at s = 3 / 4.
Journal ArticleDOI
M-strings, Elliptic Genera and N=4 String Amplitudes
Stefan Hohenegger,Amer Iqbal +1 more
TL;DR: In this paper, the authors study mass-deformed N = 2 gauge theories from various points of view, including (p, q)-brane webs in type II string theory using Nekrasov's instanton calculus, (refined) topological string using the topological vertex formalism and M theory via the elliptic genus of certain M-strings configurations.
Journal ArticleDOI
Generalized Mathieu Moonshine
TL;DR: The Mathieu twisted twining genera as mentioned in this paper were constructed for the elliptic genus of K3 and they satisfy the expected consistency conditions, and their behaviour under modular transformations is controlled by a 3-cocycle in H-3(M-24, U(1)), just as for the case of holomorphic orbifolds.
Posted Content
Much ado about Mathieu
TL;DR: In this article, it was shown that the resulting sequence of class functions are true characters of M24, proving the Eguchi-Ooguri-Tachikawa conjecture and identifying the role group cohomology plays in both K3-Mathieu moonshine and Monstrous Moonshine.
Journal ArticleDOI
Umbral Moonshine and K3 Surfaces
TL;DR: In this article, the authors established a uniform relation between all 23 cases of umbral moonshine and K3 sigma models, and thereby took a first step in placing umbral moonhine into a geometric and physical context.
References
More filters
Book ChapterDOI
Branes within branes
TL;DR: In this article, it was shown that the BPS states (those in reduced multiplets of supersymmetry) are equally fundamental to strong-weak coupling duality and to resolving singularities.
Journal ArticleDOI
Elliptic genera of symmetric products and second quantized strings
TL;DR: In this paper, the authors proved an identity that equates the elliptic genus partition function of a supersymmetric sigma model on the N-fold symmetric product M N /SN of a manifold M to the partition function for a second quantized string theory on the space M × S 1, where the generating function of these elliptic genera is shown to be an automorphic form for O(3,2, Z).
Journal ArticleDOI
Counting dyons in N = 4 string theory
TL;DR: In this article, the degeneracy of dyons in four-dimensional N = 4 string theory has been studied in terms of a generalized super Kac-Moody algebra.
Journal ArticleDOI
The Betti numbers of the Hilbert scheme of points on a smooth projective surface
TL;DR: In this paper, the Betti number of a smooth projective variety over C or over 1 is computed using the Weil conjectures and the Picard group of S tnl.