Abstract
We propose graphs, the Combined Fiber Diagrams (CFD), to characterize all 5d superconformal field theories (SCFTs) that arise as S1-reductions of 6d SCFTs. Transitions between CFDs encode mass deformations that trigger RG-flows between SCFTs. They provide a combinatorial classification of all such 5d SCFTs and encode physical information about the strongly coupled theories, like the superconformal flavor symmetry and BPS states. We consistently reproduce known results, but more importantly predict new theories and strong coupling effects in 5d SCFTs.
Highlights
5d N = 1 SCFTs are intrinsically non-perturbative quantum field theories. At low energies these can have effective descriptions in terms of weakly coupled gauge theories, to interpolate between the infrared (IR) and ultraviolet (UV) fixed points requires methods beyond ordinary field theory, motivating a string theoretic approach. 5d theories have been engineered in string theory by (p, q)-fivebrane webs [1], or M-theory on non-compact Calabi–Yau threefolds with canonical singularities [2,3]
There is a elegant correspondence between geometry and physics, whereby the resolution of the singularity may be identified with a renormalization group (RG)-flow from the UV to an effective IR description
We define for each SCFT a graph, the combined fiber diagram (CFD), which encodes key properties of the geometry
Summary
5d N = 1 SCFTs are intrinsically non-perturbative quantum field theories At low energies these can have effective descriptions in terms of weakly coupled gauge theories, to interpolate between the infrared (IR) and ultraviolet (UV) fixed points requires methods beyond ordinary field theory, motivating a string theoretic approach. In the smooth phase, when these surfaces have finite volume, their geometry determines the low-energy gauge theory descriptions for the SCFT, if one exists Complex curves inside these surfaces determine the spectrum of matter hypermultiplets, as well as additional non-perturbative states, all of which become part of the BPS spectrum in the SCFT limit, where the surfaces collapse. In a second companion paper [15], the focus is the gauge description on the Coulomb branch of 5d SCFTs, using the methods developed in [16], complementing the CFD approach in cases lacking a gauge description
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