Interpolating Wilson loops and enriched RG flows

TL;DR

This paper introduces new interpolating Wilson loops in ABJ(M) theory, analyzes their RG flows, and demonstrates how these flows connect known BPS loops, revealing enriched supersymmetric structures and fixed points.

Contribution

It constructs a family of interpolating Wilson loops and studies their RG flows, revealing new fixed points and enriched supersymmetry in ABJ(M) theory.

Findings

Identified non-trivial beta functions for interpolating parameters.

Established RG flows connecting 1/6 BPS to 1/2 BPS loops.

Proved a g-theorem relating UV and IR Wilson loop expectation values.

Abstract

We study new $1/24$ BPS circular Wilson loops in ABJ(M) theory, which are defined in terms of several parameters that continuously interpolate between previously known $1/6$ BPS loops (both bosonic and fermionic) and $1/2$ BPS fermionic loops. We compute the expectation value of these operators up to second order in perturbation theory using a one-dimensional effective field theory approach. Within dimensional regularization, we find non-trivial $\beta$-functions for the parameters, which are marginally relevant deformations triggering RG flows from a UV fixed point represented by the $1/6$ BPS bosonic loop to an IR fixed point represented by a $1/2$ BPS fermionic loop. Generically, along all flows at least one supercharge of the theory is preserved, so that we refer to them as enriched RG flows. In particular, fixed points are connected through $1/6$ BPS fermionic operators. This holds at framing zero, which is a consequence of the regularization scheme employed. We also establish a g-theorem, relating the expectation values of the Wilson loops corresponding to the UV and IR fixed points of the flow, and discuss the one-dimensional defect SCFT living on the Wilson loop contour.