Defects in the long-range O(N) model

TL;DR

This paper explores the nature of extended defects in the long-range O(N) model, proposing three innovative methods to define and analyze line and surface defects amid the model's non-locality.

Contribution

It introduces three novel approaches for constructing and studying defects in the long-range O(N) model, addressing challenges posed by non-local interactions.

Findings

Proposed a perturbative RG approach with an additional parameter.

Developed a non-local defect coupling framework for defect CFTs.

Constructed semiclassical line defects with quantum corrections.

Abstract

We initiate the study of extended excitations in the long-range O(N) model. We focus on line and surface defects and we discuss the challenges of a naive generalization of the simplest defects in the short-range model. To face these challenges we propose three alternative realizations of defects in the long-range model. The first consists in introducing an additional parameter in the perturbative RG flow or, equivalently, treating the non-locality of the model as a perturbation of the local four-dimensional theory. The second is based on the introduction of non-local defect degrees of freedom coupled to the bulk and it provides some non-trivial defect CFTs also in the case of a free bulk, i.e. for generalized free field theory. The third approach is based on a semiclassical construction of line defects. After finding a non-trivial classical field configuration we consider the fluctuation Lagrangian to obtain quantum corrections for the defect theory.