Exploring Defects with Degrees of Freedom in Free Scalar CFTs

TL;DR

This paper constructs and analyzes various conformal defects in free scalar CFTs across different dimensions, exploring their interactions, fixed points, and correlation functions to deepen understanding of defect phenomena in conformal theories.

Contribution

It introduces new conformal defect constructions in free scalar CFTs, including interacting setups with minimal models and monodromy defects, and provides detailed correlation function analyses.

Findings

Identification of quadratic and interacting defect configurations.

Discovery of new IR defect fixed points.

Explicit calculations of correlation functions and defect central charges.

Abstract

Defects in conformal field theories are interesting objects to study from both formal and applied points of view. In this paper, we construct conformal defects in free scalar field CFTs in diverse dimensions. After discussing the possible quadratic defects, we explore interacting setups. These are realized by coupling the bulk free scalar to lower-dimensional theories, including the unitary family of minimal models $\mathcal{M}(p, p+1)$. Another example involves coupling to a two-dimensional free scalar field, from which we construct surface defects for the bulk dimensions three and five. Additionally, we consider monodromy defects associated with a global $U(1)$ flavour symmetry. In these theories, we study both self-defect interactions and couplings to Minimal Models, finding new IR defect fixed points. For all our examples, we provide results for correlation functions, such as those involving the bulk stress tensor and the displacement operator, and for the defect central charges.