Exact Bremsstrahlung and Effective Couplings

TL;DR

This paper computes exact effective couplings in certain supersymmetric theories using localization, enabling precise comparisons of observables like radiation and entanglement entropy between different supersymmetric models across all coupling regimes.

Contribution

It introduces interpolating functions for effective couplings in $ ext{N}=2$ SCFTs derived from localization, connecting weak and strong coupling regimes and generalizing known results from $ ext{N}=4$ SYM.

Findings

Derived exact effective couplings $f(g^2)$ for $ ext{N}=2$ SCFTs.

Connected $ ext{N}=2$ observables to $ ext{N}=4$ SYM results via these couplings.

Provided insights into the finite renormalization between theories.

Abstract

We calculate supersymmetric Wilson loops on the ellipsoid for a large class of $\mathcal{N}=2$ SCFT using the localization formula of Hama and Hosomichi. From them we extract the radiation emitted by an accelerating heavy probe quark as well as the entanglement entropy following the recent works of Lewkowycz-Maldacena and Fiol-Gerchkovitz-Komargodski. Comparing our results with the $\mathcal{N}=4$ SYM ones, we obtain interpolating functions $f(g^2)$ such that a given $\mathcal{N}=2$ SCFT observable is obtained by replacing in the corresponding $\mathcal{N}=4$ SYM result the coupling constant by $f(g^2)$. These "exact effective couplings" encode the finite, relative renormalization between the $\mathcal{N}=2$ and the $\mathcal{N}=4$ gluon propagator, they interpolate between the weak and the strong coupling. We discuss the range of their applicability.