On a 5D UV completion of Argyres-Douglas theories

A bstract We discuss a novel UV completion of a class of Argyres-Douglas (AD) theories in the Ω-background by its embedding into the renormalisation group flow from five dimensional $$ \mathcal{N}=1 $$ N = 1 superconformal field theories (SCFT) on S 1 . This is obtained via analysing these theories in the light of ( q -)Painlevé/gauge theory correspondence, which allows to compute the five dimensional BPS partition functions as an expansion in the Wilson loop vev with integer q -polynomials coefficients. These are derived formulating the gauge theory on a blown-up geometry and using a five-dimensional lift of (topological) operator/state correspondence. We discuss in detail the phase diagram of the four dimensional limits, pinpointing the special AD loci. Explicit computations are reported for $$ {\overset{\sim }{E}}_1 $$ E ~ 1 SCFT and its limit to H 0 = ( A 1 , A 2 ) AD theory.