Infrared enhancement of supersymmetry in four dimensions

TL;DR

This paper investigates a class of RG flows in four-dimensional N=2 SCFTs that lead to supersymmetry enhancement in the infrared, providing a new understanding and criteria for this phenomenon.

Contribution

It offers a detailed mechanism and a simple criterion for supersymmetry enhancement in 4D N=2 SCFTs, bypassing the need for a-maximization, and proposes an algorithm to find UV completions.

Findings

Established a criterion for supersymmetry enhancement

Analyzed the role of 't Hooft anomalies and superconformal algebra

Proposed an algorithm for identifying UV completions

Abstract

We study a recently-found class of RG flows in four dimensions exhibiting enhancement of supersymmetry in the infrared, which provides a lagrangian description of several strongly-coupled N=2 SCFTs. The procedure involves starting from a N=2 SCFT, coupling a chiral multiplet in the adjoint representation of the global symmetry to the moment map of the SCFT and turning on a nilpotent expectation value for this chiral. In this note we show that, combining considerations based on 't Hooft anomaly matching and basic results about the N=2 superconformal algebra, it is possible to understand in detail the mechanism underlying this phenomenon and formulate a simple criterion for supersymmetry enhancement which allows us to bypass the analysis with a-maximization. As a byproduct, we propose an algorithm to identify a lagrangian UV completion of a given N=2 SCFT under an RG flow of this type, provided there is one.