Classifying 5d SCFTs via 6d SCFTs: rank one

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.

Fibers add flavor. Part I. Classification of 5d SCFTs, flavor symmetries and BPS states

“…In this smooth space, one can in principle read off all necessary physical data such as the effective gauge descriptions and their mass deformations. There are ongoing efforts, for example in [73,74], towards classifying the smooth geometries associated with marginal theories arising from 6d SCFTs classified by F-theory.…”

Fibers add flavor. Part II. 5d SCFTs, gauge theories, and dualities

“…In that paper it was shown that if a 5d single gauge node quiver was to lead to an interacting SCFT in the UV then the matter content (and where relevant the Chern-Simons level) must satisfy the 12 We remind the reader that by a "pure-gauge" quiver we mean a quiver consisting only of gauge nodesthere remain bifundamental matter fields between these gauge nodes. 13 For low ranks these constraints will, in fact, generally be enough to completely fix Qs.…”

“…Below each embedding of the BG-CFD into the marginal CFD we list the classical flavor symmetry. and only allows gauge descriptions with gauge and flavor ranks given by (r G , r F ) =(5,13) .…”

Complete prepotential for 5d $$ \mathcal{N} $$ = 1 superconformal field theories

“…For Case 3, the parameter region should be further divided into two parts as 16) in the Weyl chamber (A.12). Finally, we discuss the conditions for physical Coulomb moduli in the different Weyl chambers of the E 8 .…”

“…As many of such 5d N = 1 theories can be engineered via Type IIB 5-brane webs [12,13] or M-theory on Calabi-Yau (CY) threefold [14,15], brane configurations also provide a direct description of the prepotential. For instance, one can study CY geometry of 5d gauge theories to obtain their triple intersections which yield the prepotential of the 5d theories or one can also scan possible gauge theory descriptions from the geometry which lead to a classification of the UV-dual theories [6,9,11,[16][17][18][19]. Though Type IIB 5branes can be understood as dual description of the geometry, not all CY geometries can be realized as a 5-brane web.…”