Wilson Loop Invariants from $W_N$ Conformal Blocks

Abstract

Knot and link polynomials are topological invariants calculated from the expectation value of loop operators in topological field theories. In 3D Chern-Simons theory, these invariants can be found from crossing and braiding matrices of four-point conformal blocks of the boundary 2D CFT. We calculate crossing and braiding matrices for $W_N$ conformal blocks with one component in the fundamental representation and another in a rectangular representation of $SU(N)$, which can be used to obtain HOMFLY knot and link invariants for these cases. We also discuss how our approach can be generalized to invariants in higher-representations of $W_N$ algebra.

20 pages, 2 figures

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Cited by in corpus (5)

• Colored knot polynomials. HOMFLY in representation [2,1]
• A slow review of the AGT correspondence
• Correlation functions with fusion-channel multiplicity in W3 Toda field theory
• Invariants of knots and links at roots of unity
• HOMFLY Polynomials of Pretzel Knots