학술논문
Wilson loop algebras and quantum K-theory for Grassmannians.
Document Type
Journal
Author
Jockers, Hans (D-BONN-P) AMS Author Profile; Mayr, Peter (D-MNCH-CTP) AMS Author Profile; Ninad, Urmi (D-BONN-P) AMS Author Profile; Tabler, Alexander (D-MNCH-CTP) AMS Author Profile
Source
Subject
14 Algebraic geometry -- 14J Surfaces and higher-dimensional varieties
14J81Relationships with physics
14Algebraic geometry -- 14M Special varieties
14M15Grassmannians, Schubert varieties, flag manifolds
81Quantum theory -- 81T Quantum field theory; related classical field theories
81T70Quantization in field theory; cohomological methods
14J81
14
14M15
81
81T70
Language
English
Abstract
Summary: ``We study the algebra of Wilson line operators in three-dimensional $\Cal N = 2$ supersymmetric ${\rm U}(M)$ gauge theories with a Higgs phase related to a complex Grassmannian ${\rm Gr}(M, N)$, and its connection to K-theoretic Gromov-Witten invariants for ${\rm Gr}(M, N)$. For different Chern-Simons levels, the Wilson loop algebra realizes either the quantum cohomology of ${\rm Gr}(M, N)$, isomorphic to the Verlinde algebra for ${\rm U}(M)$, or the quantum K-theoretic ring of Schubert structure sheaves studied by mathematicians, or closely related algebras.''