1. Schur Quantization and Complex Chern-Simons theory
- Author
-
Gaiotto, Davide and Teschner, Jörg
- Subjects
High Energy Physics - Theory ,Mathematics - Quantum Algebra - Abstract
Any four-dimensional Supersymmetric Quantum Field Theory with eight supercharges can be associated to a certain complex symplectic manifold called the "K-theoretic Coulomb branch" of the theory. The collection of K-theoretic Coulomb branches include many complex phase spaces of great interest, including in particular the "character varieties" of complex flat connections on a Riemann surface. The SQFT definition endows K-theoretic Coulomb branches with a variety of canonical structures, including a deformation quantization. In this paper we introduce a canonical "Schur" quantization of K-theoretic Coulomb branches. It is defined by a variant of the Gelfand-Naimark-Segal construction, applied to protected Schur correlation functions of half-BPS line defects. Schur quantization produces an actual quantization of the complex phase space. As a concrete application, we apply this construction to character varieties in order to quantize Chern-Simons gauge theory with a complex gauge group. Other applications include the definition of a new quantum deformation of the Lorentz group, and the solution of certain spectral problems via dualities., Comment: 114 pages, 2 figures. v2: removed a paragraph from the Introduction
- Published
- 2024