Defects in scalar field theories, RG flows and Dimensional Disentangling

TL;DR

This paper analyzes defect operators in scalar field theories near four and six dimensions, computing their RG flows and fixed points, revealing a factorization property that separates epsilon dependence from coupling dependence.

Contribution

It introduces a double scaling limit simplifying the quantum defect theory to a classical one, and computes two-loop beta functions showing fixed point behavior and a novel factorization property.

Findings

Fixed points can move and merge, leading to annihilation.

The epsilon dependence factorizes from coupling dependence.

The defect RG flows exhibit a remarkable disentangling property.

Abstract

We consider defect operators in scalar field theories in dimensions $d=4-\epsilon $ and $d=6-\epsilon$ with self-interactions given by a general marginal potential. In a double scaling limit, where the bulk couplings go to zero and the defect couplings go to infinity, the bulk theory becomes classical and the quantum defect theory can be solved order by order in perturbation theory. We compute the defect $\beta $ functions to two loops and study the Renormalization Group flows. The defect fixed points can move and merge, leading to fixed point annihilation; and they exhibit a remarkable factorization property where the $\epsilon$-dependence gets disentangled from the coupling dependence.