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Branes and DAHA Representations.

Bibliographic Details
Main Author: Gukov, Sergei.
Other Authors: Koroteev, Peter., Nawata, Satoshi., Pei, Du., Saberi, Ingmar.
Format: eBook
Language:English
Published: Cham : Springer, 2023.
Edition:1st ed.
Series:SpringerBriefs in Mathematical Physics Series
Subjects:
Electronic books.
Online Access:Click to View
Table of Contents:
  • Intro
  • Contents
  • 1 Introduction
  • 1.1 Background
  • 1.2 Results
  • 1.3 Structure
  • 2 2d Sigma-Models and DAHA
  • 2.1 Higgs Bundles and Flat Connections
  • 2.2 DAHA of Rank One and Its Spherical Algebra
  • 2.3 Canonical Coisotropic Branes in A-models
  • 2.3.1 Spherical DAHA as the Algebra of (mathfrakBcc,mathfrakBcc)-Strings
  • 2.4 Lagrangian A-Branes and Modules of mathscrOq(mathfrakX)
  • 2.5 (A,B,A)-Branes for Polynomial Representations
  • 2.6 Branes with Compact Supports and Finite-Dimensional Representations: Object Matching
  • 2.6.1 Generic Fibers of the Hitchin Fibration
  • 2.6.2 Irreducible Components in Singular Fibers of Type I2
  • 2.6.3 Moduli Space of G-Bundles
  • 2.6.4 Exceptional Divisors
  • 2.7 Bound States of Branes and Short Exact Sequences: Morphism Matching
  • 2.7.1 At Singular Fiber of Type I2
  • 2.7.2 At Global Nilpotent Cone of Type I0*
  • 3 3d Theories and Modularity
  • 3.1 DAHA and Modularity
  • 3.1.1 SU(2): Refined Chern-Simons and TQFT Associated to Argyres-Douglas Theory
  • 3.1.2 SU(N): Higher Rank Generalization
  • 3.2 Relation to Skein Modules and MTC[M3]
  • 4 4d Theories, Fivebranes, and M-Theory
  • 4.1 Coulomb Branches of 4d N=2* Theories of Rank One
  • 4.2 Algebra of Line Operators
  • 4.3 Including Surface Operator
  • Appendix A Glossary of Symbols
  • Appendix B Basics of DAHA
  • B.1 DAHA
  • B.1.1 Double Affine Braid Group and Double Affine Weyl Group
  • B.1.2 PBW Theorem for DAHA
  • B.1.3 Spherical Subalgebra
  • B.1.4 Braid Group and SL(2,mathbbZ) Action
  • B.1.5 Polynomial Representation of DAHA
  • B.1.6 Symmetric Bilinear Form
  • B.1.7 Degenerations
  • B.2 DAHA of Type A1
  • B.2.1 Polynomial Representation
  • B.2.2 Functional Representation
  • B.2.3 Trigonometric Cherednik Algebra of Type A1
  • B.2.4 Rational Cherednik Algebra of Type A1
  • Appendix C Quantum Torus Algebra.
  • C.1 Representations of Quantum Torus Algebra
  • C.1.1 Unitary Representations
  • C.1.2 Non-unitary Representations
  • C.1.3 Geometric Viewpoint
  • C.2 Branes for Quantum Torus Algebra
  • C.2.1 Cyclic Representations
  • C.2.2 Polynomial Representations
  • C.3 Symmetrized Quantum Torus
  • C.3.1 Representation Theory
  • C.3.2 Corresponding Branes
  • Appendix D 3d mathcalN=4 Theories and Cherednik Algebras
  • D.1 Coulomb Branches of 3d mathcalN=4 Theories
  • D.2 3d mathcalN=4 Coulomb Branches and Cherednik Algebras
  • Appendix References.

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