Line Defects with a Cusp in Fermionic CFTs

TL;DR

This work analyzes line defects with a cusp in interacting fermionic CFTs at GN/GNY-type fixed points, computing the cusp anomalous dimension $\Gamma_{\mathbf{h}_1\mathbf{h}_2}(\theta)$ using $\epsilon$-expansion near $d=4$ and large-$N$ methods for $2<d<4$. The authors derive explicit expressions for $\Gamma$ in the GNY model and its generalizations to $N_s$ scalars, enabling extraction of defect data such as defect-changing and creation operator dimensions, Casimir energies in defect fusion, and normalization constants of displacement and tilt correlators; they also provide Padé-resummed estimates in $d=3$. Cross-checks include large-$N$ consistency, reductions to known $O(N)$ and Ising limits, and comparisons with related defect setups. The results establish a controlled framework to connect defect fusion, symmetry breaking on the defect, and integrated correlators in fermionic dCFTs, with potential implications for condensed matter systems and holographic contexts. Overall, the paper provides new, quantitative defect data for fermionic line defects, obtained through complementary perturbative and large-$N$ techniques, and demonstrates how cusp observables encode rich information about the dCFT data.

Abstract

We study line defects with a cusp in fermionic CFTs arising as fixed points of scalar-fermion theories with Yukawa interactions. These include the Gross-Neveu-Yukawa model and some of its generalizations with additional scalar fields, which can be thought of as UV completions of fermionic theories with quartic interactions. We compute the cusp anomalous dimension in these models to one-loop order in the epsilon expansion near four dimensions, and also to leading order in the large $N$ expansion in $2<d<4$. We discuss several observables that can be extracted from the cusp anomalous dimension, such as the dimensions of the defect changing and defect creation operators, the Casimir energy appearing in the fusion of defects, and the normalization coefficients of the two-point functions of displacement and tilt operators. We provide some estimates of the values of these observables in $d=3$ using the one-loop epsilon expansion and Padé approximants.

Figures (15)

• Figure 1.1: Cusp at angle $\theta$ with two different defect couplings on each arm.
• Figure 1.2: The two defects $a$ and $b$ with cusp angle $\theta\rightarrow 0$ can be described as two line defects $a$ and $\bar{b}$ fusing.
• Figure 2.1: Diagrams contributing to the cusp anomalous dimension to $\mathcal{O}(\epsilon)$.
• Figure 2.2: Self-energy contributions to $\mathcal{O}(\epsilon)$.
• Figure 2.3: Diagram contributing to the cusp anomalous dimension to leading order at large $N$.