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arXiv · 2009.12243

Yang-Yang functions, Monodromy and knot polynomials

Peng Liu·Wei-Dong Ruan
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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.

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Peng Liu, Wei-Dong Ruan. 2020-09-25. Yang-Yang functions, Monodromy and knot polynomials. https://doi.org/10.1007/jhep03(2021)033

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