Wilson loops and defect RG flows in ABJM

Abstract

Abstract We continue our study of renormalization group (RG) flows on Wilson loop defects in ABJM theory, which we have initiated in arXiv:2211.16501 . We generalize that analysis by including non-supersymmetric fixed points and RG trajectories. To this end, we first determine the “ordinary”, non-supersymmetric Wilson loops, which turn out to be two and to include an R-symmetry preserving coupling to the scalar fields of the theory, contrary to their four-dimensional counterpart defined solely in terms of the gauge field holonomy. We then deform these operators by turning on bosonic and/or fermionic couplings, which trigger an elaborate, multi-dimensional network of possible RG trajectories connecting a large spectrum of fixed points classified in terms of the amount (possibly zero) of supersymmetry and R-symmetry preserved. The β-functions are computed to leading order in the ABJM coupling but exactly in the deformation parameters, using an auxiliary one-dimensional theory on the defect and a dimensional regularization scheme. A striking result is the different behavior of the two ordinary Wilson loops, of which one turns out to be a UV unstable point while the other is IR stable. The same is true for the two 1/2 BPS Wilson loops. We interpret our results from a defect CFT (dCFT) point of view, computing the anomalous dimensions of the operators associated to the deformations and establishing appropriate g-theorems. In particular, the fermionic unstable fixed point is associated to a dCFT which is not reflection positive.

Keywords

• Chern-Simons Theories
• Renormalization Group
• Wilson, ’t Hooft and Polyakov loops