Fibers add Flavor, Part II: 5d SCFTs, Gauge Theories, and Dualities

TL;DR

This paper advances the understanding of 5d superconformal field theories by linking geometric graph methods with gauge theory descriptions, enabling systematic enumeration of gauge theories and revealing new dualities.

Contribution

It connects combined fiber diagrams with gauge theory quivers, allowing systematic classification and discovery of dualities in 5d SCFTs.

Findings

CFDs are consistent with gauge theory descriptions.

Systematic enumeration of gauge theories for a given SCFT.

Identification of new UV-dualities through graph embeddings.

Abstract

In arXiv:1906.11820 and arXiv:1907.05404 we proposed an approach based on graphs to characterize 5d superconformal field theories (SCFTs), which arise as compactifications of 6d $\mathcal{N}= (1,0)$ SCFTs. The graphs, so-called combined fiber diagrams (CFDs), are derived using the realization of 5d SCFTs via M-theory on a non-compact Calabi--Yau threefold with a canonical singularity. In this paper we complement this geometric approach by connecting the CFD of an SCFT to its weakly coupled gauge theory or quiver descriptions and demonstrate that the CFD as recovered from the gauge theory approach is consistent with that as determined by geometry. To each quiver description we also associate a graph, and the embedding of this graph into the CFD that is associated to an SCFT provides a systematic way to enumerate all possible consistent weakly coupled gauge theory descriptions of this SCFT. Furthermore, different embeddings of gauge theory graphs into a fixed CFD can give rise to new UV-dualities for which we provide evidence through an analysis of the prepotential, and which, for some examples, we substantiate by constructing the M-theory geometry in which the dual quiver descriptions are manifest.