BPS Algebras in 2D String Theory
Journal article, 2022

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 V1⊗ V¯ 2, where V1, V2 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.


Sarah M. Harrison

McGill University

N. M. Paquette

Institute for Advanced Studies

Daniel Persson

Chalmers, Mathematical Sciences, Algebra and geometry

R. Volpato

Istituto Nazionale Di Fisica Nucleare, Sezione di Padova

Annales Henri Poincare

1424-0637 (ISSN) 1424-0661 (eISSN)

Vol. 23 3667-3752

Subject Categories

Algebra and Logic


Mathematical Analysis



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