Emitted Radiation in Superconformal Field Theories

TL;DR

This paper reviews how emitted radiation from accelerated particles in superconformal field theories can be computed using Wilson loops, defect CFT techniques, and supersymmetric localization, highlighting differences between $ =4$ and $ =2$ theories.

Contribution

It provides a comprehensive review of methods to compute emitted radiation in superconformal theories, emphasizing the relation between Bremsstrahlung functions and Wilson loop expectation values.

Findings

Relation between Bremsstrahlung function and stress tensor coefficient.

Exact results for emitted radiation in supersymmetric theories.

Differences in radiation properties between $ =4$ and $ =2$ SCFTs.

Abstract

The computation of the emitted radiation by an accelerated external particle can be addressed in a gauge theory with the insertion of a Wilson loop. With the addition of conformal symmetry this problem is consistently formalized in terms of correlation functions in presence of the Wilson loop, which are constrained by defect CFT techniques. In theories with extended supersymmetry we can also resort to supersymmetric localization on a four-sphere. By using this set of tools, we review the close relation between the Bremsstrahlung function and the stress energy tensor one-point coefficient in abelian theories and in superconformal field theories. After presenting the state of the art for generic CFTs, we mainly focus on the supersymmetric cases. We discuss the differences between the maximally supersymmetric $\mathcal{N}=4$ case and $\mathcal{N}=2$ SCFTs, and finally we review the general and exact result for the emitted radiation in terms of a first order derivative of the Wilson loop expectation value on a squashed sphere.