On the Algebras of BPS States
Copyright policy )On the Algebras of BPS States
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.
43 pages, harvmac (b), no figures. References added. We clarify the use of the term GKM
- University of Chicago United States
- University of New Haven United States
- Yale University United States
High Energy Physics - Theory, Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations, Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory), FOS: Physical sciences, String and superstring theories; other extended objects (e.g., branes) in quantum field theory, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics, Relationships between surfaces, higher-dimensional varieties, and physics, Relationship to Lie algebras and finite simple groups, Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras, Mathematics - Algebraic Geometry, High Energy Physics - Theory (hep-th), FOS: Mathematics, Applications of compact analytic spaces to the sciences, Algebraic Geometry (math.AG)
High Energy Physics - Theory, Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations, Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory), FOS: Physical sciences, String and superstring theories; other extended objects (e.g., branes) in quantum field theory, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics, Relationships between surfaces, higher-dimensional varieties, and physics, Relationship to Lie algebras and finite simple groups, Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras, Mathematics - Algebraic Geometry, High Energy Physics - Theory (hep-th), FOS: Mathematics, Applications of compact analytic spaces to the sciences, Algebraic Geometry (math.AG)
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