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 $$ \mathcal{N}=1 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:math> 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 $$ {\overset{\sim }{E}}_1 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>E</mml:mi> <mml:mo>~</mml:mo> </mml:mover> <mml:mn>1</mml:mn> </mml:msub> </mml:math> SCFT and its limit to H 0 = ( A 1 , A 2 ) AD theory.