RG flows with supersymmetry enhancement and geometric engineering

TL;DR

The paper develops a geometric-engineering framework to study infrared supersymmetry enhancement in 4d N=2 SCFTs with ADE global symmetry. By analyzing the D_k^b(J) family realized via hypersurface singularities and establishing an IR duality to J^b(k) fixed points, it provides a uniform mechanism for susy-enhancing RG flows and a direct link between UV/IR Seiberg–Witten data. It identifies explicit Seiberg–Witten curves for classical and exceptional cases, clarifies when lagrangian UV completions exist, and uncovers numerous new nonlagrangian examples, alongside implications for chiral algebras. The work offers a systematic, geometry-driven route to predict IR fixed points, relate SW data across scales, and unify prior results on susy enhancement.

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.