Codimension one defects in free scalar field theory

TL;DR

This paper explores various properties of codimension one defects in free scalar field theory, including conformal, topological, and non-conformal defects, through analytical methods and explicit computations.

Contribution

It provides a comprehensive analysis of defects in free scalar theories, combining matching conditions and perturbation resummation to compute diverse observables.

Findings

Explicit formulas for correlators in the presence of defects

Calculation of defect anomalous dimensions and fusion rules

Analysis of entanglement entropy and defect stability

Abstract

We study various aspects of codimension one defects in free scalar field theory, with particular emphasis on line defects in two-dimensions. These defects are generically non-conformal, but include conformal and topological defects as special cases. Our analysis is based on the interplay between two complementary descriptions, the first involving matching conditions imposed on fields and their derivatives across the defect, and the second on the resummation of perturbation theory in terms of renormalized defect couplings. Using either description as appropriate we compute a variety of observables: correlators of fields in the presence of such defects; the defect anomalous dimension; multiple defects and their fusion; canonical quantization and instabilities; ring shaped defects with application to the g-theorem and the entanglement entropy of accelerating defects; defects on the torus and Cardy formulas for the asymptotic density of states of the defect Hilbert space; and quenches produced by spacelike defects. The simplicity of the model allows for explicit computation of all these quantities, and provides a starting point for more complicated theories involving interactions.