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 the 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.
Highlights
With the addition of conformal symmetry, this problem is consistently formalized in terms of correlation functions in the presence of the Wilson loop, which are constrained by defect CFT techniques
The main goal of this paper is to review the computation of the Wilson loop observables related to the emitted energy problem in four dimensional superconformal field theories with extended (N ≥ 2) supersymmetry
While this problem is solvable for abelian gauge theories, it definitely becomes less trivial for non-abelian theories, where the addition of superconformal symmetry is needed to produce exact results in the coupling constant
Summary
Probe the vacuum with a cusped Wilson line representing the world line of a classical charged particle moving with constant velocity v1μ that suddenly changes to v2μ due to instantaneous acceleration. Expanding the result for small angles, from (2) and (9), we read the Bremsstrahlung as an exact function in the electric charge: BMax e2 12π 2 For this simple theory, the relation between the Bremsstrahlung function (and the emitted energy) with the stress tensor one-point function can be verified explicitly. Starting from the Maxwell stress energy tensor, it is possible to evaluate it on the explicit solution for the gauge field Aμ in the presence of a source, given by the Lienard–Wiechert retarded potential, see [36–39] for a thorough analysis From this solution, it is possible to extract the one-point coefficient hW [16]:. Two independent computations determine both the Bremsstrahlung function B and the stress tensor coefficient hW for the abelian Maxwell theory in the presence of an external particle These observables are functions of the coupling, in this case, the electric charge e and a simple relation between the two quantities holds:
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