Abstract
In [1, 2] 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.
Highlights
Supersymmetric gauge theories are an ideal setup to explore strongly-coupled aspects of quantum field theories
In [1, 2] we proposed an approach based on graphs to characterize 5d superconformal field theories (SCFTs), which arise as compactifications of 6d N = (1, 0) SCFTs
Different embeddings of gauge theory graphs into a fixed combined fiber diagrams (CFDs) 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
Summary
Supersymmetric gauge theories are an ideal setup to explore strongly-coupled aspects of quantum field theories. Coulomb branches, dualities and CFDs. The strength of the approach that we proposed in [1, 2] lies in its combinatorial nature, which at the same time captures the network of 5d SCFTs that descend from a 6d theory, and the flavor symmetry of the UV-fixed point. There are 6d theories, where no known elliptic fibration in terms of a Weierstrass model for the fully singular geometry exists In such instances we can turn the arguments around and use our approach to constrain the marginal CFD, by using known gauge theory descriptions as well as flavor symmetry enhancements of the 5d descendants. This is done for all types of gauge theories and matter in 5d that have an SCFT in the UV. Our focus will be to characterize the Coulomb branch of a 5d gauge theory with matter, using the underlying representation-theoretic structure, based on the classic [40] as well as the box graph description in [44]
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