On a 5D UV completion of Argyres-Douglas theories

TL;DR

This paper presents a new ultraviolet completion of certain Argyres-Douglas theories by embedding them into five-dimensional superconformal field theories, utilizing Painlevé/gauge theory correspondence to compute BPS partition functions.

Contribution

It introduces a novel 5D UV completion of AD theories through RG flow analysis and Painlevé/gauge correspondence, providing explicit computations and phase diagram insights.

Findings

Computed 5D BPS partition functions as q-polynomial expansions.

Analyzed phase diagrams and identified AD loci.

Explicitly studied the $ ilde E_1$ SCFT and its AD limit.

Abstract

We discuss a novel UV completion of a class of Argyres-Douglas (AD) theories in the $\Omega$-background by its embedding into the renormalisation group flow from five dimensional $\mathcal{N}=1$ superconformal field theories (SCFT) on $S^1$. This is obtained via analysing these theories in the light of ($q$-)Painlev\'e/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 $\tilde E_1$ SCFT and its limit to H$_0=(A_1,A_2)$ AD theory.