Bremsstrahlung function in 𝒩 = 2 SCFTs far beyond the supergravity limit

A bstract We study the Bremsstrahlung function in two four-dimensional 𝒩 = 2 superconformal gauge theories: the E -theory, with hypermultiplets in the symmetric and antisymmetric representations, and the D -theory, with antisymmetric and fundamental matter. Using matrix-model techniques, we derive exact results at arbitrary coupling for the first few orders in the large- N expansion. At leading order, both theories are shown to be planar equivalent to 𝒩 = 4 Super Yang-Mills, while beyond the planar limit their behavior differs significantly. For the E -theory, we prove that the subleading correction is exactly given by a derivative of the free energy with respect to the coupling. This relation enables us to determine the complete strong-coupling expansion for the Bremsstrahlung function, including non-perturbative contributions, by exploiting known results for the free energy. For the D -theory, the exact expressions have a more intricate structure. We perform a detailed analysis of the strong-coupling regime of the subleading large- N corrections, showing that, in this case, there are expansions in inverse powers of the coupling which truncate after finitely many terms. We further analyze the non-perturbative effects at strong coupling and derive closed-form expressions also for these contributions. These results provide precise predictions for the holographic duals of both theories beyond the supergravity approximation, probing higher orders in the large- N expansion and the full subleading corrections at strong coupling.