On the classification of 5d SCFTs

Lakshya Bhardwaj

doi:10.1007/jhep09(2020)007

Abstract

We determine all 5d SCFTs upto rank three by studying RG flows of 5d KK theories. Our analysis reveals the existence of new rank one and rank two 5d SCFTs not captured by previous classifications. In addition to that, we provide for the first time a systematic and conjecturally complete classification of rank three 5d SCFTs. Our methods are based on a recently studied geometric description of 5d KK theories, thus demonstrating the utility of these geometric descriptions. It is straightforward, though computationally intensive, to extend this work and systematically classify 5d SCFTs of higher ranks (greater than or equal to four) by using the geometric description of 5d KK theories.

Highlights

This conjecture was tested successfully in a geometric context in [8]
Our analysis reveals the existence of new rank one and rank two 5d SCFTs not captured by previous classifications
We provide for the first time a systematic and conjecturally complete classification of rank three 5d SCFTs

Summary

Introduction

This conjecture was tested successfully in a geometric context in [8]. There a classification of shrinkable smooth local Calabi-Yau threefolds was performed such that compactifying M-theory on such a threefold would give rise to a 5d SCFT of rank less than or equal to two. Carrying out the blowdown produces the geometry x dP1+1 y which is a new rank one 5d SCFT not discussed in the literature before.7 The only possible flow removes the self-gluing from (2.53) giving rise to the 5d SCFT described by (2.35) discovered earlier. Blowing down x in the right surface of (3.37) and blowing down m number of blowups in the left surface of (3.37), we discover a series of 5d SCFTs described by the geometries

Objectives

Results

Conclusion