On the algebras of BPS states

Details On the algebras of BPS states On the algebras of BPS states

1996-09-01

arxiv.org/abs/hep-th/9609017v2

Commun.Math.Phys.197:489-519,1998

Physics

High Energy Physics

High Energy Physics - Theory

43 pages, harvmac (b), no figures. References added. We clarify the use of the term GKM

Scientific paper

10.1007/s002200050461

We define an algebra on the space of BPS states in theories with extended supersymmetry. We show that the algebra of perturbative BPS states in toroidal compactification of the heterotic string is closely related to a generalized Kac-Moody algebra. We use D-brane theory to compare the formulation of RR-charged BPS algebras in type II compactification with the requirements of string/string duality and find that the RR charged BPS states should be regarded as cohomology classes on moduli spaces of coherent sheaves. The equivalence of the algebra of BPS states in heterotic/IIA dual pairs elucidates certain results and conjectures of Nakajima and Gritsenko & Nikulin, on geometrically defined algebras and furthermore suggests nontrivial generalizations of these algebras. In particular, to any Calabi-Yau 3-fold there are two canonically associated algebras exchanged by mirror symmetry.

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