The large-$N$ limit of the 4d $\mathcal{N}=1$ superconformal index

Understand

We systematically analyze the large-$N$ limit of the superconformal index of $\mathcal{N}=1$ superconformal theories having a quiver description.

• The index of these theories is known in terms of unitary matrix integrals, which we calculate using the recently-developed technique of elliptic extension.
• This technique allows us to easily evaluate the integral as a sum over saddle points of an effective action in the limit where the rank of the gauge group is infinite.
• For a generic quiver theory under consideration, we find a special family of saddles whose effective action takes a universal form controlled by the anomaly coefficients of the theory.