Abstract
A class of 4d mathcal{N}=3 SCFTs can be obtained from gauging a discrete subgroup of the global symmetry group of mathcal{N}=4 Super Yang-Mills theory. This discrete subgroup contains elements of both the SU(4) R-symmetry group and the SL(2, ℤ) S-duality group of mathcal{N}=4 SYM. We give a prescription for how to perform the discrete gauging at the level of the superconformal index and Higgs branch Hilbert series. We interpret and match the information encoded in these indices to known results for rank one mathcal{N}=3 theories. Our prescription is easily generalised for the Coulomb branch and the Higgs branch indices of higher rank theories, allowing us to make new predictions for these theories. Most strikingly we find that the Coulomb branches of higher rank theories are generically not-freely generated.
Highlights
The first to seriously consider the consequences of N = 3 supersymmetry was [1] who, via the study of N = 3 superconformal symmetry, were able to reveal several basic properties, which consistent N = 3 theories should possess, if they exist
A class of 4d N = 3 SCFTs can be obtained from gauging a discrete subgroup of the global symmetry group of N = 4 Super Yang-Mills theory
We explicitly computed the Coulomb branch limit of the index as well as the Higgs branch Hilbert series for a number of theories based on laced groups
Summary
In comparison with the discussion (2.6)–(2.8) this Zn global symmetry acts non-trivially on multiple Coulomb branch operators of the parent theory, namely. We would like to point out that in [3] discrete gauging which results in non-freely generated Coulomb branches was explicitly not considered. They considered discrete gauging of the parent theories SkN, of only Zp ⊂ Zk/ discrete symmetry which acts non-trivially only on a single Coulomb branch operator. Upon the Zn discrete gauging psu(2, 2|4) superconformal symmetry is broken down to su(2, 2|3) (for n = 3, 4, 6) Representations of this algebra are labelled by (E, j1, j2, R1, R2, rN =3) of the maximal compact bosonic subalgebra u(1)E ⊕ su(2)1 ⊕ su(2)2 ⊕ su(3) ⊕ u(1)rN=3 ⊂ su(2, 2|3).
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