BPS Hall Algebra of Scattering Hall States

Abstract

Starting with a very pedestrian point of view we compare two different at the first glance definitions for an algebra associated to BPS states in supersymmetric fields theories. One proposed by Harvey and Moore exploits $S$-matrices of BPS states as structure constants of a new algebra. Another one proposed by Kontsevich and Soibelman gives a construction according to the structure of cohomological Hall algebras. We show these two constructions give equivalent algebras.

31 pages, 4 figures

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Cited by in corpus (10)

• Quiver Yangian from Crystal Melting
• Quiver Yangian and Supersymmetric Quantum Mechanics
• Toroidal and Elliptic Quiver BPS Algebras and Beyond
• 3d $\mathcal{N}=4$ Gauge Theories on an Elliptic Curve
• BPS Algebras in 2D String Theory
• BPS States Meet Generalized Cohomology
• More on Affine Dynkin Quiver Yangians
• Wall-Crossing Effects on Quiver BPS Algebras
• Weyl Mutations in Quiver Yangians
• Quiver Yangian algebras associated to Dynkin diagrams of A-type and their rectangular representations