HOMFLY Polynomial from a Generalized Yang–Yang Function

Abstract

Starting from the free field realization of Kac–Moody Lie algebra, we define a generalized Yang–Yang function. Then for the Lie algebra of type $A_{n}$, we derive braiding and fusion matrix by braiding the thimble from the generalized Yang–Yang function. One can construct a knots invariant H(K) from the braiding and fusion matrix. It is an isotropy invariant and obeys a skein relation. From them, we show that the corresponding knots invariant is HOMFLY polynomial.

Keywords

Yang–Yang function / Thimbles / HOMFLY polynomials