5d SCFTs and their non-supersymmetric cousins

TL;DR

This paper explores non-supersymmetric deformations of 5d superconformal field theories, analyzing their stability, dualities, and phase transitions, and proposing potential non-supersymmetric 5d conformal field theories.

Contribution

It generalizes supersymmetry-breaking deformations to higher rank 5d SCFTs and classifies their phase structure using UV dualities and Chern-Simons level jumps.

Findings

One-to-one correspondence between non-SUSY deformations and (p,q) 5-brane webs.

Identification of phase transitions involving Chern-Simons level jumps.

Proposal of candidate non-SUSY 5d CFTs based on phase diagram analysis.

Abstract

We consider generalisations of the recently proposed supersymmetry breaking deformation of the 5d rank-1 $E_1$ superconformal field theory to higher rank. We generalise the arguments to theories which admit a mass deformation leading to gauge theories coupled to matter hypermultiplets at low energies. These theories have a richer space of non-supersymmetric deformations, due to the existence of a larger global symmetry. We show that there is a one-to-one correspondence between the non-SUSY deformations of the gauge theory and their $(p,q)$ 5-brane web. We comment on the (in)stability of these deformations both from the gauge theory and the 5-brane web point of view. UV duality plays a key role in our analysis, fixing the effective Chern-Simons level for the background vector multiplets, together with their complete prepotential. We partially classify super-Yang-Mills theories known to enjoy UV dualities which show a phase transition where different phases are separated by a jump of Chern-Simons levels of both a perturbative and an instantonic global symmetry. When this transition can be reached by turning on a non-supersymmetric deformation of the UV superconformal field theory, it can be a good candidate to host a 5d non-supersymmetric CFT. We also discuss consistency of the proposed phase diagram with the 't Hooft anomalies of the models that we analyse.