Abstract
We refine our previous proposal [1-3] for systematically classifying 4d rank-1 $$ \mathcal{N} $$ = 2 SCFTs by constructing their possible Coulomb branch geometries. Four new recently discussed rank-1 theories [4, 5], including novel $$ \mathcal{N} $$ = 3 SCFTs, sit beautifully in our refined classification framework. By arguing for the consistency of their RG flows we can make a strong case for the existence of at least four additional rank-1 SCFTs, nearly doubling the number of known rank-1 SCFTs. The refinement consists of relaxing the assumption that the flavor symmetries of the SCFTs have no discrete factors. This results in an enlarged (but finite) set of possible rank-1 SCFTs. Their existence can be further constrained using consistency of their central charges and RG flows.
Highlights
We refine our previous proposal [1,2,3] for systematically classifying 4d rank1 N = 2 SCFTs by constructing their possible Coulomb branch geometries
In [2] we classified potential rank-1 Coulomb branch geometries of SCFTs by constructing possible inequivalent regular special Kähler mass deformations of scale-invariant Kodaira singularities. The list of such deformations is given in table 1 of [2], where we identified the flavor symmetry algebra, f, of the SCFTs associated to each geometry
In [5], by looking at the D4 6d (2, 0) SCFT twisted and compactified on 3-punctured spheres (“fixtures”) with puncture boundary conditions including Z3 outer-automorphism twists of D4, Chacaltana, Distler, and Trimm find a new rank-1 SCFT with central charges a = 25/8, c = 7/2, Coulomb branch (CB) parameter of dimension ∆(u) = 6, and flavor algebra f = A3 with flavor central charge k = 14
Summary
Theories supported by new evidence are shaded blue and un-shaded rows are for already established SCFTs. fourth line of table 1. The [II ∗ , G2 ] does not flow to a [III ∗ , u(1) ⋊ Z2 ]. But to a [III ∗ , A1 ] which is an alternative good interpretation of the former. The other good theories not shown in table 1 are similar alternative A1 interpretations of the u(1)⋊Z2 theories. We should note that the interpretation — discussed at length in [2] — of the frozen. I1∗ and I0∗ singularities as weakly gauged rank-0 SCFTs is not considered here. I1∗ singularity we focus only on the more conservative interpretation of this singularity as the lagrangian su(2) gauge theory with a single half-hypermultiplet in the spin-3/2
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