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.
Highlights
Mixing matrix of anomalous dimensions of planar N = 2 SCFTs is obtained by the N = 4 SYM result after replacing the N = 4 SYM coupling constant g2 by an effective coupling f, a function of all the marginal couplings gi2 of the N = 2 SCFT, computed via localization in [2]
We calculate supersymmetric Wilson loops on the ellipsoid for a large class of N = 2 SCFT using the localization formula of Hama and Hosomichi
Searching for more observables O to which the coupling substitution rule can be applied, we compute via localization the large N limit of the b-deformed BPS Wilson loops of [14] for a large class3 of N = 2 SCFT, the quiver diagram of which is depicted in figure 1
Summary
We present for the convenience of the reader a short review of the main ingredients appearing in this paper. We introduce the cusp anomalous dimension as well as the Bremsstrahlung function. We explain how to obtain the Bremsstrahlung function in N = 2 SCFTs using localization and the work of [19]. We review our previous work on the coupling substitution rule in the spectral problem of the purely gluonic sector of N = 2 SCFTs and show how it can be computed
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