Natural Construction of Ten Borcherds-Kac-Moody Algebras Associated with Elements in $$M_{23}$$

Möller, Sven

doi:10.1007/s00220-021-04018-w

Cited by 2 publications

(1 citation statement)

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“…Conjecturally, there is only one additional isomorphism class V Γ 1,1 ⊗ V where V is a self-dual VOA of c = 24 without currents -it is the case where V = V ♮ is the Monster VOA [30]. From each of these isomorphism classes of vertex algebras, one can define a BKM algebra using Borcherds' construction based on chiral bosonic string theory compactified on V Γ 1,1 ⊗ V ; see [9,10,41,42,22,51] for explicit descriptions and denominator identities. 12 It is natural to conjecture that by tensoring any self-dual VOA of c = 24 with the bosonic (non-chiral) CFT on a circle S 1 , one gets one of precisely 12 distinct CFTs of left and right central charges (25,1).…”

Section: Cartan Torus the Final Results Is The Weyl Denominator Of Th...mentioning

confidence: 99%

BPS Algebras in 2D String Theory

Harrison,

Paquette,

Persson

et al. 2021

Preprint

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We discuss a set of heterotic and type II string theory compactifications to 1+1 dimensions that are characterized by factorized internal worldsheet CFTs of the form V 1 ⊗ V2 , where V 1 , V 2 are self-dual (super) vertex operator algebras. In the cases with spacetime supersymmetry, we show that the BPS states form a module for a Borcherds-Kac-Moody (BKM) (super)algebra, and we prove that for each model the BKM (super)algebra is a symmetry of genus zero BPS string amplitudes. We compute the supersymmetric indices of these models using both Hamiltonian and path integral formalisms. The path integrals are manifestly automorphic forms closely related to the Borcherds-Weyl-Kac denominator. Along the way, we comment on various subtleties inherent to these low-dimensional string compactifications.

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Section: Cartan Torus the Final Results Is The Weyl Denominator Of Th...mentioning

confidence: 99%

BPS Algebras in 2D String Theory

Harrison,

Paquette,

Persson

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

BPS Algebras in 2D String Theory

Harrison

Paquette

Persson

et al. 2022

Ann. Henri Poincaré

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We discuss a set of heterotic and type II string theory compactifications to $$1+1$$ 1 + 1 dimensions that are characterized by factorized internal worldsheet CFTs of the form $$V_1\otimes \bar{V}_2$$ V 1 ⊗ V ¯ 2 , where $$V_1, V_2$$ V 1 , V 2 are self-dual (super) vertex operator algebras. In the cases with spacetime supersymmetry, we show that the BPS states form a module for a Borcherds–Kac–Moody (BKM) (super)algebra, and we prove that for each model the BKM (super)algebra is a symmetry of genus zero BPS string amplitudes. We compute the supersymmetric indices of these models using both Hamiltonian and path integral formalisms. The path integrals are manifestly automorphic forms closely related to the Borcherds–Weyl–Kac denominator. Along the way, we comment on various subtleties inherent to these low-dimensional string compactifications.

show abstract

Natural Construction of Ten Borcherds-Kac-Moody Algebras Associated with Elements in $$M_{23}$$

Cited by 2 publications

References 50 publications

BPS Algebras in 2D String Theory

BPS Algebras in 2D String Theory

BPS Algebras in 2D String Theory

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