Strong-coupling results in (non-)conformal $\mathcal{N}=2$ theories with fundamental flavors

We study a class of four-dimensional $\mathcal{N}=2$ SU($N$) gauge theories with two massless hypermultiplets in the rank-two antisymmetric representation and $0\leq N_f\leq 4$ fundamental flavors. These theories are superconformal for $N_f=4$ and asymptotically free otherwise. Supersymmetric localization on the four-sphere applies in both cases and leads to matrix-model representations for a broad class of protected observables. Within this framework, we compute the free energy and the expectation value of the $\frac{1}{2}$-BPS circular Wilson loop in the large-$N$ limit. For any $N_f$, we show that the infinite series of non-planar corrections at large 't Hooft coupling $\lambda$ can be resummed in terms of an effective coupling $\widetilde{\lambda}$. In the non-conformal window ($0\leq N_f<4$), this provides a first example in which localization leads to explicit results in the planar limit at strong 't Hooft coupling. In the superconformal case ($N_f=4$), the large-$N$ expansion in $\widetilde{\lambda}$ suggests a refined AdS/CFT dictionary in which $\widetilde{\lambda}$, rather than $\lambda$, plays the role of the bulk string coupling.