Linking loops in ABJM and refined theory

TL;DR

This paper computes link averages of Wilson loops in ABJM theory using localization, introduces a refined version of the theory, and explores their algebraic and topological properties.

Contribution

It develops a matrix integral approach for link averages in ABJM theory and proposes a refined model with new link average computations.

Findings

Derived a supermatrix integral for Wilson loop averages

Established a factorization property and Verlinde formula in supergroup sectors

Computed refined link averages in the proposed refined ABJM theory

Abstract

We consider the link average of the half-BPS Wilson loop operators in N = 6 superconformal Chern-Simons-matter theory, which is called ABJM theory. We show that this loop average is reduced to a (super)matrix integral by the localization method, in a similar way to the bosonic U(N) Chern-Simons theory. Using this matrix integral, we compute the two- and three-link averages with an operator formalism inspired by a three-dimensional topological field theory. We obtain a factorization of the link average, and the Verlinde formula in a sector of supergroup representations. We also propose a refined version of ABJM theory, and compute some refined link averages.