Continuous Quivers

We consider half-BPS Wilson loops in $\mathcal{N} = 2$ long circular quiver gauge theories at large-$N$ with continuous limit shape of 't Hooft couplings. In the limit of an infinite number of nodes $L$, the solution to the localisation matrix model is given by Wigner semicircles for any profile of couplings. Higher-order corrections in $1/L$ can be calculated iteratively. Combining large $L$ with a strong coupling regime we identify a double scaling limit that describes dynamics along a fifth dimension which emerges dynamically from the quiver diagram. We solve the resulting integro-differential equation exactly for a certain range of parameters.