Yang-Yang functions, Monodromy and knot polynomials

Abstract

We derive a structure of $\mathbb{Z}[t,t^{-1}]$-module bundle from a family of Yang-Yang functions. For the fundamental representation of the complex simple Lie algebra of classical type, we give explicit wall-crossing formula and prove that the monodromy representation of the $\mathbb{Z}[t,t^{-1}]$-module bundle is equivalent to the braid group representation induced by the universal R-matrices of $U_h(g)$. We show that two transformations induced on the fiber by the symmetry breaking deformation and respectively the rotation of two complex parameters commute with each other.

References in corpus (8)

• Gaudin Model, Bethe Ansatz and Critical Level
• Darboux coordinates, Yang-Yang functional, and gauge theory
• Knot Invariants from Four-Dimensional Gauge Theory
• Quasiclassical asymptotics of solutions to the KZ equations
• Quantum Integrable Model of an Arrangement of Hyperplanes
• Free field realizations in representation theory and conformal field theory
• On the Gaudin model associated to Lie algebras of classical types
• Kauffman polynomial from a generalized Yang-Yang function