Abstract
We systematically analyse 5d superconformal field theories (SCFTs) obtained by dimensional reduction from 6d mathcal{N} = (1, 0) SCFTs. Such theories have a realization as M-theory on a singular Calabi-Yau threefold, from which we determine the so-called combined fiber diagrams (CFD) introduced in [1–3]. The CFDs are graphs that encode the superconformal flavor symmetry, BPS states, low energy descriptions, as well as descendants upon flavor matter decoupling. To obtain a 5d SCFT from 6d, there are two approaches: the first is to consider a circle-reduction combined with mass deformations. The second is to circle-reduce and decouple an entire gauge sector from the theory. The former is applicable e.g. for very Higgsable theories, whereas the latter is required to obtain a 5d SCFT from a non-very Higgsable 6d theory. In the M-theory realization the latter case corresponds to decompactification of a set of compact surfaces in the Calabi-Yau threefold. To exemplify this we consider the 5d SCFTs that descend from non-Higgsable clusters and non-minimal conformal matter theories. Finally, inspired by the quiver structure of 6d theories, we propose a gluing construction for 5d SCFTs from building blocks and their CFDs.
Highlights
5d superconformal field theories (SCFTs) are intrinsically non-perturbative
We will require a detailed knowledge of the geometry to compute the multiplicity factors, which are key to deriving the labels of the unmarked vertices with n > −1, we can determine the part of the combined fiber diagrams (CFD), that encodes the superconformal flavor symmetry as well as the mass deformations (i.e. the (−1) vertices)
In this paper we investigate the possible ways of getting 5d superconformal field theories (SCFTs) coming from 6d on a circle
Summary
5d superconformal field theories (SCFTs) are intrinsically non-perturbative. For instance, 5d gauge theories become strongly coupled in the UV and they can only be low-energy effective descriptions of the putative superconformal field theories. The CFDs defined in [1] encode key non-perturbative information of the theory and the trees of descendant 5d SCFTs with the same dimension of the Coulomb branch (rank) This approach is always applicable in the case of so-called very Higgsable 6d theories [47], i.e. geometries where the base of the elliptic fibration is smooth. If there is no consistent assignment of ruling and section curves that apply to all Si · Sj, the theory does not have a gauge description In the singular limit, when vol(S) → 0, the state obtained by an M2-brane wrapping C decouples
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