Phases of 5d SCFTs from M-/F-theory on non-flat fibrations

Abstract

We initiate the systematic investigation of non-flat resolutions of non-minimal singularities in elliptically fibered Calabi-Yau threefolds. Compactification of M-theory on these geometries provides an alternative approach to studying phases of five-dimensional superconformal field theories (5d SCFTs). We argue that such resolutions capture non-trivial holonomies in the circle reduction of the 6d conformal matter theory that is the F-theory interpretation of the singular fibration. As these holonomies become mass deformations in the 5d theory, non-flat resolutions furnish a novel method in the attempt to classify 5d SCFTs through 6d SCFTs on a circle. A particularly pleasant aspect of this proposal is the explicit embedding of the 5d SCFT’s enhanced flavor group inside that of the parent 6d SCFT, which can be read off from the geometry. We demonstrate these features in toric examples which realize 5d theories up to rank four.

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

“…A further set of constraints, which we refer to as the "constraints on the number of hypermultiplets", comes from the analysis of single gauge node quivers in [9]. 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.…”

“…To begin with, we briefly recall the necessary background material on non-minimal singularities in elliptic fibrations, their (possibly non-flat) resolutions, and their role in engineering 5d SCFTs, and refer to [2,12] for more details.…”

“…The key proposal of [12] to read off the flavor symmetry geometrically, which was systematized and condensed into CFDs in [1,2], is to track how the non-compact divisors D (ν) i intersect S. More precisely, these divisors are P 1 -fibered over a non-compact curve W ν ⊂ B.…”

“…In recent works [1,2] we proposed an alternative approach that arose out of the wellestablished geometric engineering via M-theory on a non-compact Calabi-Yau threefolds [8][9][10]12,[39][40][41][42]. One of the key insights of [1,2] is that there is a succinct description of the CFT data in terms of graphs, and transitions between graphs correspond to mass deformations and subsequent RG-flows.…”

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

“…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.…”