A Borcherds–Kac–Moody Superalgebra with Conway Symmetry

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

doi:10.1007/s00220-019-03518-0

Cited by 13 publications

(30 citation statements)

References 74 publications

(223 reference statements)

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“…Similarly, the theories V f E 8 , V f , F 24 all naturally occur as (chiral halves) of worldsheet CFTs at special points in the moduli space of maximally supersymmetric type II string compactifications to 2d. We expect that the BKM superalgebras constructed in [31,48], and this paper, occur as algebras acting on spacetime BPS states at such special points. This is a notion we make precise in upcoming work [30].…”

Section: Jhep02(2021)039mentioning

confidence: 74%

“…a sense, a 'chiral version' of that construction -and is a supersymmetric generalization of Borcherds' construction of the fake Monster and Monster Lie algebras [5,7] that was inspired by bosonic string theory. The main steps have been developed in [48] for the specific example where V is the lattice SVOA V f E 8 based on the E 8 lattice, and has been generalized to the example where V = V f in [31]. We will briefly describe the main steps in this construction and refer to [31,40,48] for the proofs of most statements.…”

Section: Jhep02(2021)039mentioning

confidence: 99%

“…The main steps have been developed in [48] for the specific example where V is the lattice SVOA V f E 8 based on the E 8 lattice, and has been generalized to the example where V = V f in [31]. We will briefly describe the main steps in this construction and refer to [31,40,48] for the proofs of most statements.…”

Section: Jhep02(2021)039mentioning

confidence: 99%

“…However, as is described in [2,15,18,19] and section 3, by gauging symmetries, one can move from one to the other. Furthermore, in [48] and [31], respectively, the theories V f E 8 and V f have been used to furnish constructions of a special type of infinite-dimensional Lie superalgebra known as a Borcherds-Kac-Moody (BKM) superalgebra. BKM algebras were originally introduced by Borcherds [7] in his proof of the monstrous moonshine conjectures of Conway and Norton [14], and Thompson [51,52].…”

Section: Introductionmentioning

confidence: 99%

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Fun with F24

Harrison

Paquette

Persson

et al. 2021

J. High Energ. Phys.

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We study some special features of F24, the holomorphic c = 12 superconformal field theory (SCFT) given by 24 chiral free fermions. We construct eight different Lie superalgebras of “physical” states of a chiral superstring compactified on F24, and we prove that they all have the structure of Borcherds-Kac-Moody superalgebras. This produces a family of new examples of such superalgebras. The models depend on the choice of an $$ \mathcal{N} $$ N = 1 supercurrent on F24, with the admissible choices labeled by the semisimple Lie algebras of dimension 24. We also discuss how F24, with any such choice of supercurrent, can be obtained via orbifolding from another distinguished c = 12 holomorphic SCFT, the $$ \mathcal{N} $$ N = 1 supersymmetric version of the chiral CFT based on the E8 lattice.

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Section: Jhep02(2021)039mentioning

confidence: 74%

Section: Jhep02(2021)039mentioning

confidence: 99%

Section: Jhep02(2021)039mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fun with F24

Harrison

Paquette

Persson

et al. 2021

J. High Energ. Phys.

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“…Conway moonshine, on the other hand, introduces a Conway module V s whose McKay-Thompson series coincide with Hauptmoduls with vanishing constant terms. It was developed in [76,77] (see also [78], [79] and [80] for nice summaries of the construction). The Conway module V s is the unique, up to isomorphisms, super-VOA (SVOA) with c V s = 12 and N = 1 superconformal structure, which has no states with weight 1/2.…”

Section: Conway Moonshinementioning

confidence: 99%

TASI Lectures on Moonshine

Cheng¹,

Anagiannis²

2018

Proceedings of Theoretical Advanced Study Institute Summer School 2017 "Physics at the Fundamental Frontier" — PoS(TASI2017)

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The word moonshine refers to unexpected relations between two distinct mathematical structures: finite group representations and modular objects. It is believed that the key to understanding moonshine is through physical theories with special symmetries. Recent years have seen a variety of new ways in which finite group representations and modular objects can be connected to each other, and these developments have brought promises but also puzzles into the string theory community. These lecture notes aim to bring graduate students in theoretical physics and mathematical physics to the forefront of this active research area. In Part II of this note, we review the various cases of moonshine connections, ranging from the classical monstrous moonshine established in the last century to the most recent findings. In Part III, we discuss the relation between the moonshine connections and physics, especially string theory. After briefly reviewing a recent physical realisation of monstrous moonshine, we will describe in some details the mystery of the physical aspects of umbral moonshine, and also mention some other setups where string theory black holes can be connected to moonshine. To make the exposition self-contained, we also provide the relevant background knowledge in Part I, including sections on finite groups, modular objects, and two-dimensional conformal field theories. This part occupies half of the pages of this set of notes and can be skipped by readers who are already familiar with the relevant concepts and techniques.

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Hecke relations among 2d fermionic RCFTs

Lee,

Sun

2023

J. High Energ. Phys.

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Recently, Harvey and Wu proposed a suitable Hecke operator for vector-valued SL(2, ℤ) modular forms to connect the characters of different 2d rational conformal field theories (RCFTs). We generalize such an operator to the 2d fermionic RCFTs and call it fermionic Hecke operator. The new Hecke operator naturally maps the Neveu-Schwarz (NS) characters of a fermionic theory to the NS characters of another fermionic theory. Mathematically, it is the natural Hecke operator on vector-valued Γθ modular forms of weight zero. We find it can also be extended to $$ \overset{\sim }{\textrm{NS}} $$ NS ~ and Ramond (R) sectors by combining the characters of the two sectors together. We systematically study the fermionic Hecke relations among 2d fermionic RCFTs with up to five NS characters and find that almost all known supersymmetric RCFTs can be realized as fermionic Hecke images of some simple theories such as supersymmetric minimal models. We also study the coset relations between fermionic Hecke images with respect to c = 12k holomorphic SCFTs.

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A Borcherds–Kac–Moody Superalgebra with Conway Symmetry

Cited by 13 publications

References 74 publications

Fun with F24

Fun with F24

TASI Lectures on Moonshine

Hecke relations among 2d fermionic RCFTs

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