Vertex Operator Algebras and the Monster

By I. Frenkel, James Lepowsky, A. Meurman. 2011

1,241 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/e1a4e2ee9b67e0a2b6adfd9ed1cafee65724809e

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Citations in the corpus

Notes on the K3 Surface and the Mathieu Group M 24 (2010, background): “It was then found [Frenkel et al. 88] that this representation is naturally associated with the two-dimensional string propagating on R(26)/Λ/Z2 , where Λ is the Leech lattice.”
A framework of Rogers–Ramanujan identities and their arithmetic properties (2014, methodology): “proofs of generalized Rogers–Ramanujan identities, and Rogers–Ramanujan-type identities for arbitrary aﬃne Lie algebras in which, typically, the sum side is replaced by a combinatorial sum, see e.g., [34, 49, 62] and references therein. In this paper we have a similar but distinct aim, namely to ﬁnd”
Lattice vertex algebras and combinatorial bases: general case and W-algebras (2012, methodology): “We equip VL with a vertex algebra structure as earlier [12, 22, 27, 15] (by choosing an appropriate 2-cocycle).”
Unitary vertex operator algebras (2013, methodology): “First, we recall some facts about Heisenberg vertex operator algebras from [FLM], [LL].”
Construction and classification of holomorphic vertex operator algebras (2015, methodology): “th the aﬃne structures A1D6,5 and A5,6C2,3A1,2. We now review the list of known holomorphic c = 24 vertex operator algebras. • 24 vertex operator algebras associated with the Niemeier lattices ([B1], [FLM], [D]), • 15 Z2-orbifolds using standard lifts of the (−1)-involution ([FLM] for the moonshine ”
Mathieu Moonshine in the elliptic genus of K3 (2010, methodology): “In the context of Monstrous Moonshine, this observation was eventually explained by the construction of the so-called Monster conformal field theory V ♮ [3], a self-dual conformal field theory at c = 24 whose space of states is of the form”
Braided Tensor Categories and Extensions of Vertex Operator Algebras (2014, methodology): “In the constructions and applications of vertex operator algebras, such algebras obtained by adjoining suitable modules to a smaller vertex operator algebra play a significant role, as in [FLM], for example.”
Quantum gravity partition functions in three dimensions (2007, background): “ function has a q−expansion J(τ) = X m≥−1 c(m)qm = 1 q +196884q + ... (6.7) where the coeﬃcients c(m) are positive integers. Our choices of overall normalization and constant term c(0) = 0 agree with [32] but diﬀer from the most classical convention. As the c(m) are positive, it follows that J obeys”
Logarithmic conformal field theory: beyond an introduction (2013, background): “Its application to the study of critical statistical models and string theory is well known, see [2–5] for example, but it also provides the basic inspiration for the mathematical theory of vertex operator algebras [6–8].”
The Structure of Parafermion Vertex Operator Algebras: General Case (2009, methodology): “We expect the reader to be familiar with the elementary theory of vertex operator algebras as found, for example, in [10] and [18].”
Simple current extensions beyond semi-simplicity (2015, background): “ture [SY, FG, GW] and have then later been introduced also for VOAs [DLM1], especially Ho¨hn was able to relate the extension problem to the categorical context [Ho¨]. The famous moonshine moduleVOAof[FLM]isasimplecurrentextensionofacertainVOA.Itcanalsobeconstructedusingvertextensorcategories[H1]. I”
Axiomatic Quantum Field Theory in Curved Spacetime (2008, background): “the one based upon the notion o f "vertex operator algebras" given in [2, 23, 11].”
Mathieu twining characters for K3 (2010, background): “One of the upshots of this analysis is that the J-function can be thought of as the partition function of a self-dual conformal field theory, the ‘Monster conformal field theory’ [3, 16], whose automorphism group is precisely the Monster group.”