Yang-Yang functions, monodromy and knot polynomials

Abstract

Abstract We derive a structure of 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 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.

Keywords

• Chern-Simons Theories
• Quantum Groups
• Spontaneous Symmetry Breaking
• Wilson
• ’t Hooft and Polyakov loops