Notes on Integral Identities for 3d Supersymmetric Dualities

Understand

Four dimensional $\mathcal{N}=2$ Argyres-Douglas theories have been recently conjectured to be described by $\mathcal{N}=1$ Lagrangian theories.

• Such models, once reduced to 3d, should be mirror dual to Lagrangian $\mathcal{N}=4$ theories.
• This has been numerically checked through the matching of the partition functions on the three sphere.
• In this article, we provide an analytic derivation for this result in the $A_n$ case via hyperbolic hypergeometric integrals.