On the algebras of BPS states

Abstract

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

Cited by in corpus (110)

• U-duality and M-Theory
• Permeable conformal walls and holography
• Split States, Entropy Enigmas, Holes and Halos
• The effective action of D7-branes in N=1 Calabi-Yau orientifolds
• The spectrum of BPS branes on a noncompact Calabi-Yau
• Open string instantons and superpotentials
• D-branes, Categories and N=1 Supersymmetry
• Matrix Models, Geometric Engineering and Elliptic Genera
• Marginal and Relevant Deformations of N=4 Field Theories and Non-Commutative Moduli Spaces of Vacua
• Instanton Strings and HyperKaehler Geometry
• Refined, Motivic, and Quantum
• Anomaly Equations and Intersection Theory
• Supersymmetric Three-cycles and (Super)symmetry Breaking
• D-Branes, Derived Categories, and Grothendieck Groups
• Mathieu twining characters for K3
• D-Brane Stability and Monodromy
• Instantons on Noncommutative R^4 and Projection Operators
• Fusion of conformal interfaces
• Mirror symmetry for open strings
• Stability and BPS branes
• The singular geometry of the sliver
• D-branes, Exceptional Sheaves and Quivers on Calabi-Yau manifolds: From Mukai to McKay
• Cohomological Hall algebras, vertex algebras and instantons
• Kaluza-Klein bundles and manifolds of exceptional holonomy
• One-Loop BPS amplitudes as BPS-state sums
• D-Branes on K3-Fibrations
• M-strings, Elliptic Genera and N=4 String Amplitudes
• Quiver Yangian from Crystal Melting
• Eisenstein series and automorphic representations
• Knots-quivers correspondence
• BPS states, knots and quivers
• M-theory and E10: Billiards, Branes, and Imaginary Roots
• D-Branes and Bundles on Elliptic Fibrations
• Topics in D-geometry
• Bound state transformation walls
• A Point's Point of View of Stringy Geometry
• Shifted Quiver Yangians and Representations from BPS Crystals
• The BPS Spectrum of N=2 SU(N) SYM and Parton Branes
• Collapsing D-Branes in Calabi-Yau Moduli Space: I
• Counting BPS states on the Enriques Calabi-Yau
• Lorentzian Lie (3-)algebra and toroidal compactification of M/string theory
• The effective action of D-branes in Calabi-Yau orientifold compactifications
• Exponential Networks and Representations of Quivers
• Four ways across the wall
• Topological strings, strips and quivers
• Rankin-Selberg methods for closed strings on orbifolds
• Twisted K-Theory of Lie Groups
• M-Theoretic Derivations of 4d-2d Dualities: From a Geometric Langlands Duality for Surfaces, to the AGT Correspondence, to Integrable Systems
• Gauge/Bethe correspondence from quiver BPS algebras
• Crystal Melting and Wall Crossing Phenomena
• Boundary Fermions, Coherent Sheaves and D-branes on Calabi-Yau manifolds
• What is the dual of a dipole?
• D-Branes on ALE Spaces and the ADE Classification of Conformal Field Theories
• Some Navigation Rules for D-Brane Monodromy
• Homological algebra of knots and BPS states
• The Uniqueness of the Abelian Born-Infeld Action
• Duality Between String Junctions and D-Branes on Del Pezzo Surfaces
• Moonshine, Superconformal Symmetry, and Quantum Error Correction
• Generalized Kac-Moody Algebras from CHL dyons
• No More Walls! A Tale of Modularity, Symmetry, and Wall Crossing for 1/4 BPS Dyons
• Quantum toroidal algebras and solvable structures in gauge/string theory
• Product-Group Unification in Type IIB String Thoery
• Variations on stability
• On the Symmetries of Classical String Theory
• A-branes, foliations and localization
• BPS Hall Algebra of Scattering Hall States
• BPS Algebras, Genus Zero, and the Heterotic Monster
• Non-linear Yang-Mills instantons from strings are $\pi$-stable D-branes
• Twisted Bundles on Noncommutative $T^4$ and D-brane Bound States
• BPS Saturated String Amplitudes: K3 Elliptic Genus and Igusa Cusp Form
• Conway Subgroup Symmetric Compactifications Of Heterotic String
• Seiberg duality for Chern-Simons quivers and D-brane mutations
• Borcherds Algebras and N=4 Topological Amplitudes
• A Note on Quiver Yangians and $\mathcal{R}$-Matrices
• K-theoretical boundary rings in N=2 coset models
• A Solution to the Decompactification Problem in Chiral Heterotic Strings
• Abelian quiver invariants and marginal wall-crossing
• BPS Algebras in 2D String Theory
• Crystal Melting, BPS Quivers and Plethystics
• Enhanced Gauge Groups in N=4 Topological Amplitudes and Lorentzian Borcherds Algebras
• C^2/Z_n Fractional branes and Monodromy
• A Borcherds-Kac-Moody superalgebra with Conway symmetry
• Functional determinants, index theorems, and exact quantum black hole entropy
• Vertical D4-D2-D0 bound states on K3 fibrations and modularity
• Quiver Yangians and $\mathcal{W}$-Algebras for Generalized Conifolds
• More on Affine Dynkin Quiver Yangians
• Charging solid partitions
• Wall-Crossing Effects on Quiver BPS Algebras
• Matrix Theory Compactification on Noncommutative $T^4/Z_2$
• BKM Lie superalgebra for the Z_5 orbifolded CHL string
• Computing Borcherds Products
• A Gaussian distribution for refined DT invariants and 3D partitions
• Fun with $F_{24}$
• Algorithms for representations of quiver Yangian algebras
• Hecke Operators on Vector-Valued Modular Forms
• Quantum Vacua of 2d Maximally Supersymmetric Yang-Mills Theory
• Landau-Ginzburg Description of D-branes on ALE Spaces
• Towards the theory of Yangians
• DT invariants from vertex algebras
• Vogel's universality and the classification problem for Jacobi identities
• An Overview of Crystals and Double Quiver Yangians
• Lattice Vertex Algebras on General Even, Self-dual Lattices
• Sigma Models for Bundles on Calabi-Yau: A Proposal for Matrix String Compactifications
• Charge functions for odd dimensional partitions
• Geometric Transitions and D-Term SUSY Breaking
• $E_9$ symmetry in the Heterotic String on $S^1$ and the Weak Gravity Conjecture
• Quiver Yangian algebras associated to Dynkin diagrams of A-type and their rectangular representations
• K-theory and phase transitions at high energies
• Duality and Combinatorics of Long Strings in ADS3
• Line bundle twisted chiral de Rham complex and bound states of D-branes on toric manifolds