Classifying 5d SCFTs via 6d SCFTs: Rank one
Lakshya Bhardwaj, Patrick Jefferson
TL;DR
This work presents a systematic program to classify 5d SCFTs by invoking circle compactifications of 6d SCFTs, including possible discrete twists. It encodes the resulting 5d KK data in a Calabi-Yau threefold $X_{ rak{T}}$, from which the 5d Coulomb-branch prepotential and BPS spectrum follow via triple intersections and fibral curves, while RG flows are realized by flopping curves in $X_{ rak{T}}$ to endpoints that are 5d SCFT geometries. The authors provide explicit constructions for untwisted rank-one 6d SCFTs in the unfrozen F-theory phase, compute the resolved CY geometries and their data, and formulate concrete criteria for end-point geometries under RG flows; they also discuss generalizations to arbitrary rank. This framework unifies geometric and field-theoretic data to map 6d information to 5d fixed points, enabling systematic classification and potential extensions to higher rank and twisted compactifications.
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.