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.

25 pages, 14 figures

References in corpus (2)

• Knot Invariants from Four-Dimensional Gauge Theory
• Schrödinger equations, deformation theory and $t{t}^{\ast }$-geometry