Wilson loop algebras and quantum K-theory for Grassmannians
Hans Jockers, Peter Mayr, Urmi Ninad, Alexander Tabler
Abstract
A bstract We study the algebra of Wilson line operators in three-dimensional $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2 supersymmetric U( M ) gauge theories with a Higgs phase related to a complex Grassmannian Gr( M, N ), and its connection to K-theoretic Gromov-Witten invariants for Gr( M, N ). For different Chern-Simons levels, the Wilson loop algebra realizes either the quantum cohomology of Gr( M, N ), isomorphic to the Verlinde algebra for U( M ), or the quantum K-theoretic ring of Schubert structure sheaves studied by mathematicians, or closely related algebras.
Topics & Concepts
PhysicsGrassmannianLoop (graph theory)Connection (principal bundle)CohomologyQuantumAlgebra over a fieldLoop algebraGauge (firearms)Ring (chemistry)Operator algebraPure mathematicsWilson loopQuantum affine algebraQuantum cohomologyGauge theoryFiltered algebraQuantum algebraAlgebra representationHiggs bosonBRST quantizationMathematical physicsSuperconformal algebraCoherent sheafStructure constantsCurrent algebraCellular algebraQuantum groupSupersymmetric gauge theoryTheoretical physicsCohomology ringPhase (matter)Particle physicsAlgebraic structures and combinatorial modelsAdvanced Operator Algebra ResearchHomotopy and Cohomology in Algebraic Topology