RG flows with supersymmetry enhancement and geometric engineering

TL;DR

This paper explores RG flows in 4d $ abla$=2 SCFTs with ADE symmetry, revealing supersymmetry enhancement, IR equivalences, and relations between UV and IR theories through geometric and algebraic methods.

Contribution

It introduces a new framework connecting geometric engineering, supersymmetry enhancement, and IR equivalences in $ abla$=2 SCFTs with ADE symmetry.

Findings

Supersymmetry enhances in the IR for a class of $ abla$=2 SCFTs.

Established IR equivalences between RG flows and $ abla$=2 preserving flows.

Derived relations between UV and IR Seiberg-Witten curves and chiral algebras.

Abstract

In this paper we study a class of $\mathcal{N}=2$ SCFTs with ADE global symmetry defined via Type IIB compactification on a class of hypersurfaces in $\mathbb{C}^3\times\mathbb{C}^*$. These can also be constructed by compactifying the 6d (2,0) theory of type ADE on a sphere with an irregular and a full punctures. When we couple to the ADE moment map a chiral multiplet in the adjoint representation and turn on a (principal) nilpotent vev for it, all the theories in this family display enhancement of supersymmetry in the infrared. We observe that all known examples of lagrangian theories which flow, upon the same type of deformation, to strongly coupled $\mathcal{N}=2$ theories fit naturally in our framework, thus providing a new perspective on this topic. We propose an infrared equivalence between this RG flow and a manifestly $\mathcal{N}=2$ preserving one and, as a byproduct, we extract a precise prescription to relate the SW curves describing the UV and IR fixed points for all theories with A or D global symmetry. We also find, for a certain subclass, a simple relation between UV and IR theories at the level of chiral algebras.