Fusion of conformal defects in four dimensions

TL;DR

This paper investigates the fusion process of two conformal defects in four-dimensional free theories as they approach each other, revealing a non-conformal effective action and implications for defect correlators.

Contribution

It introduces a path integral approach to analyze defect fusion and demonstrates the emergence of non-conformal effective actions in the fusion limit.

Findings

Fusion leads to a non-conformal effective defect action.

Two-point defect correlators cannot generally be decomposed into conformal defect contributions.

Path integral formalism effectively describes defect fusion process.

Abstract

We consider two conformal defects close to each other in a free theory, and study what happens as the distance between them goes to zero. This limit is the same as zooming out, and the two defects have fused to another defect. As we zoom in we find a non-conformal effective action for the fused defect. Among other things this means that we cannot in general decompose the two-point correlator of two defects in terms of other conformal defects. We prove the fusion using the path integral formalism by treating the defects as sources for a scalar in the bulk.