Microstate Counting via Bethe Ans\"{a}tze in the 4d ${\cal N}=1$ Superconformal Index

Understand

We study the superconfomal index of four-dimensional toric quiver gauge theories using a Bethe Ansatz approach recently applied by Benini and Milan.

• Relying on a particular set of solutions to the corresponding Bethe Ansatz equations we evaluate the superconformal index in the large $N$ limit, thus avoiding to take any Cardy-like limit.
• We present explicit results for theories arising as a stack of $N$ D3 branes at the tip of toric Calabi-Yau cones: the conifold theory, the suspended pinch point gauge theory, the first del Pezzo theory and $Y^{p,q}$ quiver gauge theories.
• For a suitable choice of the chemical potentials of the theory we find agreement with predictions made for the same theories in the Cardy-like limit.