Monstrous BPS-Algebras and the Superstring Origin of Moonshine

Paquette, Natalie M.; Persson, Daniel; Volpato, Roberto

doi:10.48550/arxiv.1601.05412

Cited by 16 publications

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In this note, we expand on some technical issues raised in [1] by the authors, as well as providing a friendly introduction to and summary of our previous work. We construct a set of heterotic string compactifications to 0+1 dimensions intimately related to the Monstrous moonshine module of Frenkel, Lepowsky, and Meurman (and orbifolds thereof).

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confidence: 99%

“…While some of the tools used in the proof were explicitly inspired by CFT and string theory, the physical interpretation of many aspects of Monstrous moonshine remains mysterious. Our work [1] is an attempt to fill in this gap.…”

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confidence: 99%

“…In our work [1], we propose a possible physical interpretation of the Monstrous moonshine conjecture in the context of heterotic strings. For each g ∈ M, we consider a certain heterotic string compactification to 0 + 1 dimensions.…”

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confidence: 99%

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BPS algebras, genus zero and the heterotic Monster

Paquette

Persson

Volpato

2017

J. Phys. A: Math. Theor.

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Abstract. In this note, we expand on some technical issues raised in [1] by the authors, as well as providing a friendly introduction to and summary of our previous work. We construct a set of heterotic string compactifications to 0+1 dimensions intimately related to the Monstrous moonshine module of Frenkel, Lepowsky, and Meurman (and orbifolds thereof). Using this model, we review our physical interpretation of the genus zero property of Monstrous moonshine. Furthermore, we show that the space of (secondquantized) BPS-states forms a module over the Monstrous Lie algebras m g -some of the first and most prominent examples of Generalized Kac-Moody algebras-constructed by Borcherds and Carnahan. In particular, we clarify the structure of the module present in the second-quantized string theory. We also sketch a proof of our methods in the language of vertex operator algebras, for the interested mathematician.

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BPS algebras, genus zero and the heterotic Monster

Paquette

Persson

Volpato

2017

J. Phys. A: Math. Theor.

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“…Conway and Norton defined Monstrous moonshine as the observation that the Fourier coefficients of the j-function decompose into dimensions of representations of the Monster group [2] and this was proven by Borcherds using generalized Kac-Moody algebras [6]. In the language of conformal field theory, Monstrous moonshine is the statement that the states of an orbifold theory, which is D = 25 + 1 bosonic string theory on (R 24 /Λ 24 )/Z 2 (where Λ 24 is the Leech lattice [4,31,32]), are organized in representations of the Monster group, with partition function equivalent to the j-function [8,12,14]. Witten also found the Monster in three-dimensional pure gravity [22], for AdS 3 , where the dual CFT is expected to be that of Frenkel, Lepowsky and Meurman [5].…”

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confidence: 99%

“…8,12,8) , It is then easy to realize that all such bosonic massless (SO 24 -covariant) fields in 25 + 1 can be uplifted to a smaller set of bosonic massless fields (SO 25 -covariant) fields in 26 + 1; namely, since , 884 degrees of freedom, is acted upon by the Monster group M, because it corresponds to the sum of its two smallest representations, namely the trivial (singlet) 1 and the non-trivial one 196, 883. Such a theory will be henceforth named Monstrous M-theory, or simply M 2 -theory.…”

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Monstrous M-theory

Marrani,

Rios,

Chester

2020

Preprint

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We define a D = 26 + 1 Monstrous, purely bosonic M-theory, whose massless spectrum, of dimension 196, 884, is acted upon by the Monster group. Upon reduction to D = 25 + 1, this gives rise to a plethora of non-supersymmetric, gravito-dilatonic theories, whose spectrum irreducibly splits under the Monster as 196, 884 = 1 ⊕ 196, 883, where the singlet is identified with the dilaton, and 196, 883 denotes the smallest non-trivial representation of the Monster. This clarifies the definition of the Monster as the automorphism of the Griess algebra, by showing that such an algebra is not merely a sum of unrelated spaces, but rather an algebra of massless states for a Monstrous M-theory, which includes Horowitz and Susskind's bosonic M-theory as a subsector. Remarkably, a certain subsector of Monstrous M-theory, when coupled to a Rarita-Schwinger massless field in 26 + 1, exhibits the same number of bosonic and fermionic degrees of freedom.

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Heterotic sigma models on T 8 and the Borcherds automorphic form Φ12

Harrison

Kachru

Paquette

et al. 2017

J. High Energ. Phys.

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Abstract:We consider the spectrum of BPS states of the heterotic sigma model with (0, 8) supersymmetry and T 8 target, as well as its second-quantized counterpart. We show that the counting function for such states is intimately related to Borcherds' automorphic form Φ 12 , a modular form which exhibits automorphy for O(2, 26; Z). We comment on possible implications for Umbral moonshine and theories of AdS 3 gravity.

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Monstrous BPS-Algebras and the Superstring Origin of Moonshine

Cited by 16 publications

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BPS algebras, genus zero and the heterotic Monster

BPS algebras, genus zero and the heterotic Monster

Monstrous M-theory

Heterotic sigma models on T 8 and the Borcherds automorphic form Φ12

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