A Bethe Ansatz Type Formula for the Superconformal Index

Inspired by recent work by Closset, Kim, and Willett, we derive a new formula for the superconformal (or supersymmetric) index of 4D \({\mathcal {N}}=1\) theories. Such a formula is a finite sum, over the solution set of certain transcendental equations that we dub Bethe Ansatz Equations, of a function evaluated at those solutions.