Magnetic quivers for rank 1 theories

Abstract

Magnetic quivers and Hasse diagrams for Higgs branches of rank 1 4d N = 2 SCFTs are provided. These rank 1 theories fit naturally into families of higher rank theories, originating from higher dimensions, which are addressed.

Magnetic lattices for orthosymplectic quivers

“…The HWG is therefore the same as (2.57). The result here is consistent with the expectation in [55] that the generalized sequence for C 5 rank 1 SCFT can be described by both a non-simply laced unitary quiver (2.55) and the magnetic quiver for twisted D-type fixture (6.4) for n even.…”

Towards a classification of rank r $$ \mathcal{N} $$ = 2 SCFTs. Part II. Special Kahler stratification of the Coulomb branch

“…The theory that we just analyzed can be obtained as a circle reduction of a 5d SCFT and it is predicted to be the second non-trivial entry of an infinite series of four dimensional N = 2 SCFT with flavor symmetry sp(n + 1) × su(2) [68] (for n = 1 the theory is simply a bunch of free hypermultiplets). The detailed analysis of the HB Hasse diagram of this series of theories is performed in [46]. For n = 3 we find perfect agreement with the Hasse diagram in figure 20.…”

“…This stratified structure is very reminiscent of the structure of nilpotent orbits of Lie algebras [40][41][42][43][44] and more generally of symplectic singularities [31,39,45], for which the existence of the stratification has been demonstrated in [32]. Symplectic singularities also play an important role in understanding Higgs branches of four dimensional N = 2 theories and these have been recently studied, for instance, in [29,46]. A crucial difference between JHEP12(2020)022 the stratification discussed here and the geometries studied in [29,46], is that in the general singular hyperkahler case considered there, the elementary slices can have arbitrarily large (quaternionic) dimension, whereas in the special Kahler case, they always have the minimal dimension allowed for a special Kahler space, i.e., one complex dimension.…”

“…Symplectic singularities also play an important role in understanding Higgs branches of four dimensional N = 2 theories and these have been recently studied, for instance, in [29,46]. A crucial difference between JHEP12(2020)022 the stratification discussed here and the geometries studied in [29,46], is that in the general singular hyperkahler case considered there, the elementary slices can have arbitrarily large (quaternionic) dimension, whereas in the special Kahler case, they always have the minimal dimension allowed for a special Kahler space, i.e., one complex dimension. In other words, the elementary slices -or equivalently the edges of the Hasse diagram -correspond to rank 1 N = 2 Coulomb branch geometries, which in turn are given by the Kodaira classification given in table 1 or its simple generalization to be described shortly in table 3, providing a very constraining picture.…”

“…This theory is conjectured to be the second non-trivial entry of an infinite series of four dimensional N = 2 SCFTs with flavor symmetry sp(n + 3) (for n = 1 the theory is simply a bunch of free hypers) [68]. The Higgs branches of this infinite series are worked out in details using the techniques of magnetic quivers in [46] and in the context of 3d N = 4 in [30] where the corresponding theory is named X 6 . Our analysis perfectly matches with their predictions suggesting that this 4d theory flows to the X 6 upon circle compactification.…”