Line defects and radiation in $\mathcal{N}=2$ theories

TL;DR

The paper addresses how energy emission by a line defect in a 4d $\mathcal{N}=2$ theory is encoded in the background stress tensor, proving the theory-independent relation $B=3h$ for any 1/2-BPS line defect. Its approach uses the displacement operator within the defect CFT framework and leverages $\mathrm{osp}(4^*|2)$ representation theory together with supersymmetric Ward identities to constrain bulk–defect couplings. The authors show that the two-point functions of the displacement multiplet and the one-point functions of the stress-tensor multiplet are fixed by $B$ and $h$, and that the bulk-to-defect couplings reduce to these two defect data. The central result $B=3h$, obtained from SUSY Ward identities, provides a robust link between Bremsstrahlung and stress-tensor data, enabling cross-checks across observables and guiding defect bootstrap analyses, with potential extensions to other dimensions and supersymmetric defects.

Abstract

We study the conformal data of a generic superconformal half-BPS line defect in a four-dimensional $\mathcal{N} = 2$ theory. We prove a theory independent relation between the one-point function of the stress tensor in the presence of the line defect and the two-point function of the displacement operator. When the defect is interpreted as a heavy charged particle in a gauge theory, the result relates the energy emitted through Bremsstrahlung with the coupling of the stress tensor to the particle at rest.