Nekrasov-Shatashvili limit of the 5D superconformal index

We consider the Nekrasov-Shatashvili limit of the five-dimensional (5D) superconformal index and propose a novel prescription for selecting the finite contributions. Applying the latter to various examples of U(1) theories, we find that the 5D Nekrasov-Shatashvili index can be reproduced using recent techniques of Cordova and Shao, who related the 4D Schur index to the Bogomol'nyi-Prasad-Sommerfield (BPS) spectrum of the theory on the Coulomb branch. In this picture, the 5D instanton solitons are interpreted as additional flavor nodes in an associated 5D BPS quiver.