BPS Algebras in 2D String Theory

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

doi:10.48550/arxiv.2107.03507

Cited by 3 publications

(4 citation statements)

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“…This led to various proposals for algebraic structures associated to BPS states in [103][104][105][106]. One curious application of these ideas is a very suggestive approach to the important problem of finding a conceptual basis for understanding the role of genus zero groups in monstrous moonshine [107][108][109]. More recently, the subject of quiver algebras associated to BPS states on D-branes has just begun to be developed [110][111][112][113][114], giving a new physical interpretation of some old constructions of Nakajima and Kontsevich-Soibelman with many promising directions for generalizations and further development.…”

Section: Algebraic Structures Associated With Supersymmetric Sectors ...mentioning

confidence: 99%

A Panorama Of Physical Mathematics c. 2022

Bah¹,

Freed²,

Moore³

et al. 2022

Preprint

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What follows is a broad-brush overview of the recent synergistic interactions between mathematics and theoretical physics of quantum field theory and string theory. The discussion is forwardlooking, suggesting potentially useful and fruitful directions and problems, some old, some new, for further development of the subject. This paper is a much extended version of the Snowmass whitepaper on physical mathematics [1].

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Section: Algebraic Structures Associated With Supersymmetric Sectors ...mentioning

confidence: 99%

A Panorama Of Physical Mathematics c. 2022

Bah¹,

Freed²,

Moore³

et al. 2022

Preprint

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show abstract

“…On another front, special low-dimensional spacetime string theory constructions [107] have been proposed to explain the genus zero properties of Monstrous [134,133] and Conway moonshines [96], with the associated BKM algebras [97,98] playing the role of BPS spectrumgenerating algebras. BKM algebras have long been suggested to furnish an algebra of BPS states in string compactifications [106,105], and it is a fascinating open possibility that moonshine groups may be best understood as symmetries of BPS algebras.…”

Section: Connections To String Theorymentioning

confidence: 99%

Snowmass White Paper: Moonshine

Harrison¹,

Harvey²,

Paquette³

2022

Preprint

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We present a brief overview of Moonshine with an emphasis on connections to physics. Moonshine collectively refers to a set of phenomena connecting group theory, analytic number theory, and vertex operator algebras or conformal field theories. Modern incarnations of Moonshine arise in various BPS observables in string theory and, via dualities, invariants in enumerative geometry. We survey old and new developments, and highlight some of the many open questions that remain.

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“…Persson and Volpato [PPV16,PPV17], which interprets m as an algebra of spontaneously broken gauge symmetries in a particular low-dimensional heterotic string compactification. (See also [HPV19,HPPV20,HPPV21,Moo93] for related results. )…”

Section: Infinite Productsmentioning

confidence: 99%

“…Is there a BKM with Th-symmetry whose twined denominator formulae agree with the graded characters of (V ♮ 3C ) ⊗3 ? Can a string theory setup, perhaps along the lines of [PPV16,PPV17] (see also [HPV19,HPPV20,HPPV21] for related work), shed additional light on these questions?…”

Section: Generalizationsmentioning

confidence: 99%

Two New Avatars of Moonshine for the Thompson Group

Duncan¹,

Harvey²,

Rayhaun³

2022

Preprint

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The Thompson sporadic group admits special relationships to modular forms of two kinds. On the one hand, last century's generalized moonshine for the monster equipped the Thompson group with a module for which the associated McKay-Thompson series are distinguished weight zero modular functions. On the other hand, Griffin and Mertens verified the existence of a module for which the McKay-Thompson series are distinguished modular forms of weight onehalf, that were assigned to the Thompson group in this century by the last two authors of this work. In this paper we round out this picture by proving the existence of two new avatars of Thompson moonshine: a new module giving rise to weight zero modular functions, and a new module giving rise to forms of weight one-half. We explain how the newer modules are relatedto the older ones by Borcherds products and traces of singular moduli. In so doing we clarify the relationship between the previously known modules, and expose a new arithmetic aspect to moonshine for the Thompson group. We also present evidence that this phenomenon extends to a correspondence between other cases of generalized monstrous moonshine and penumbral moonshine, and thereby enriches these phenomena with counterparts in weight one-half and weight zero, respectively.

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BPS Algebras in 2D String Theory

Cited by 3 publications

References 61 publications

A Panorama Of Physical Mathematics c. 2022

A Panorama Of Physical Mathematics c. 2022

Snowmass White Paper: Moonshine

Two New Avatars of Moonshine for the Thompson Group

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