Abstract
A large class of 5d superconformal field theories (SCFTs) can be constructed by integrating out BPS particles from 6d SCFTs compactified on a circle. We describe a general method for extracting the flavor symmetry of any 5d SCFT lying in this class. For this purpose, we utilize the geometric engineering of 5d mathcal{N} = 1 theories in M-theory, where the flavor symmetry is encoded in a collection of non-compact surfaces.
Highlights
We will approach this topic from the point of view of the construction of 5d SCFTs in terms of M-theory compactified on Calabi-Yau threefolds2 (CY3)
We will restrict ourselves to the sub-class of those 5d SCFTs which can be obtained by integrating out BPS particles from the extended Coulomb branch of a known 6d SCFT compactified on a circle
M2 branes wrapping the fibers of such compact surfaces give rise to W-bosons for the gauge algebra, and M2 branes wrapping the base curves of these compact surfaces give rise to instantonic BPS particles whose mass is controlled by the inverse gauge coupling of the gauge algebra
Summary
The starting point of our analysis of flavor symmetry of 5d SCFTs is the flavor symmetry of 6d SCFTs. In this paper, we describe 6d SCFTs9 in terms of their tensor branch data which can be captured in terms of a graph. We describe 6d SCFTs9 in terms of their tensor branch data which can be captured in terms of a graph. The flavor symmetry of 6d SCFTs can be classified into two types: localized and delocalized. Localized flavor symmetries are associated to a single node or edge in the graph associated to the 6d SCFT, and delocalized flavor symmetries are associated to multiple edges and nodes in the graph associated to 6d SCFTs. as discussed in the introduction, we will only need to focus on the non-abelian part of the flavor symmetry for the purposes of this paper. We will often use the term “flavor symmetry” even when we are talking about non-abelian part of the flavor symmetry. The precise meaning of the phrase “flavor symmetry” should be clear from the context of discussion
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