The topological line of ABJ(M) theory

TL;DR

This paper constructs and analyzes the topological sector of ABJ(M) theory, providing evidence for the relation between topological operator correlators and derivatives of the mass-deformed partition function, with explicit two-loop results.

Contribution

It offers the first non-trivial proof of the relation between topological correlators and the mass derivatives in ABJ(M) theory, including explicit two-loop calculations and potential for localization.

Findings

Two-loop two-point function matches matrix model expansion

Explicit two-loop expression for the central charge c_T

Confirmation of the relation through three- and four-point functions

Abstract

We construct the one-dimensional topological sector of $\mathcal N = 6$ ABJ(M) theory and study its relation with the mass-deformed partition function on $S^3$. Supersymmetric localization provides an exact representation of this partition function as a matrix integral, which interpolates between weak and strong coupling regimes. It has been proposed that correlation functions of dimension-one topological operators should be computed through suitable derivatives with respect to the masses, but a precise proof is still lacking. We present non-trivial evidence for this relation by computing the two-point function at twoloop, successfully matching the matrix model expansion at weak coupling and finite ranks. As a by-product we obtain the two-loop explicit expression for the central charge $c_T$ of ABJ(M) theory. Three- and four-point functions up to one-loop confirm the relation as well. Our result points towards the possibility to localize the one-dimensional topological sector of ABJ(M) and may also be useful in the bootstrap program for 3d SCFTs.