Classifying 5d SCFTs via 6d SCFTs: Rank one

TL;DR

This paper presents a systematic method to classify five-dimensional superconformal field theories (5d SCFTs) by analyzing six-dimensional SCFTs compactified on a circle, utilizing geometric and RG flow techniques.

Contribution

It introduces a general procedure for deriving 5d SCFTs from 6d SCFTs via circle compactification and geometric transitions, with explicit calculations for rank one cases.

Findings

Explicit Calabi-Yau geometries for rank one 5d SCFTs

Criteria for RG flows via curve flopping in Calabi-Yau threefolds

Framework applicable to arbitrary rank generalizations

Abstract

Following a recent proposal, we delineate a general procedure to classify 5d SCFTs via compactifications of 6d SCFTs on a circle (possibly with a twist by a discrete global symmetry). The path from 6d SCFTs to 5d SCFTs can be divided into two steps. The first step involves computing the Coulomb branch data of the 5d KK theory obtained by compactifying a 6d SCFT on a circle of finite radius. The second step involves computing the limit of the KK theory when the inverse radius along with some other mass parameters is sent to infinity. Under this RG flow, the KK theory reduces to a 5d SCFT. We illustrate these ideas in the case of untwisted compactifications of rank one 6d SCFTs that can be constructed in F-theory without frozen singularities. The data of the corresponding KK theory can be packaged in the geometry of a Calabi-Yau threefold that we explicitly compute for every case. The RG flows correspond to flopping a collection of curves in the threefold and we formulate a concrete set of criteria which can be used to determine which collection of curves can induce the relevant RG flows, and, in principle, to determine the Calabi-Yau geometries describing the endpoints of these flows. We also comment on how to generalize our results to arbitrary rank.