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Magnetic quivers and Hasse diagrams for Higgs branches of rank $r$ 4d $mathcal{N}=2$ SCFTs arising from $mathbb{Z}_{ell}$ $mathcal{S}$-fold constructions are discussed. The magnetic quivers are derived using three different methods: 1) Using clues like dimension, global symmetry, and the folding parameter $ell$ to guess the magnetic quiver. 2) From 6d $mathcal{N}=(1,0)$ SCFTs as UV completions of 5d marginal theories, and specific FI deformations on their magnetic quiver, which is further folded by $mathbb{Z}_{ell}$. 3) From T-duality of Type IIA brane systems of 6d $mathcal{N}=(1,0)$ SCFTs and explicit mass deformation of the resulting brane web followed by $mathbb{Z}_{ell}$ folding. A choice of the ungauging scheme, either on a long node or on a short node, yields two different moduli spaces related by an orbifold action, thus suggesting a larger set of SCFTs in four dimensions than previously expected.
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A local SL(2,Z) transformation on the Type IIB brane configuration gives rise to an interesting class of superconformal field theories, known as the S-fold CFTs. Previously it has been proposed that the corresponding quiver theory has a link involving the T(U(N)) theory. In this paper, we generalise the preceding result by studying quivers that contain a T(G) link, where G is self-dual under S-duality. In particular, the cases of G = SO(2N), USp(2N) and G_2 are examined in detail. We propose the theories that arise from an appropriate insertion of an S-fold into a brane system, in the presence of an orientifold threeplane or an orientifold fiveplane. By analysing the moduli spaces, we test such a proposal against its S-dual configuration using mirror symmetry. The case of G_2 corresponds to a novel class of quivers, whose brane construction is not available. We present several mirror pairs, containing G_2 gauge groups, that have not been discussed before in the literature.
For any gauge theory, there may be a subgroup of the gauge group which acts trivially on the matter content. While many physical observables are not sensitive to this fact, the identification of the precise gauge group becomes crucial when the magnetic spectrum of the theory is considered. This question is addressed in the context of Coulomb branches for $3$d $mathcal{N}=4$ quiver gauge theories, which are moduli spaces of dressed monopole operators. Since monopole operators are characterized by their magnetic charge, the identification of the gauge group is imperative for the determination of the magnetic lattice. It is well-known that the gauge group of unframed unitary quivers is the product of all unitary nodes in the quiver modded out by the diagonal $mathrm{U}(1)$ acting trivially on the matter representation. This reasoning generalises to the notion that a choice of gauge group associated to a quiver is given by the product of the individual nodes quotiented by any subgroup that acts trivially on the matter content. For unframed (unitary-) orthosymplectic quivers composed of $mathrm{SO}(textrm{even})$, $mathrm{USp}$, and possibly $mathrm{U}$ gauge nodes, the maximal subgroup acting trivially is a diagonal $mathbb{Z}_2$. For unframed unitary quivers with a single $mathrm{SU}(N)$ node it is $mathbb{Z}_N$. We use this notion to compute the Coulomb branch Hilbert series of many unitary-orthosymplectic quivers. Examples include nilpotent orbit closures of the exceptional E-type algebras and magnetic quivers that arise from brane physics. This includes Higgs branches of theories with 8 supercharges in dimensions $4$, $5$, and $6$. A crucial ingredient in the calculation of exact refined Hilbert series is the alternative construction of unframed magnetic quivers from resolved Slodowy slices, whose Hilbert series can be derived from Hall-Littlewood polynomials.
Enhancement of global symmetry and supersymmetry in the infrared is one of the most intriguing phenomena in quantum field theory. We investigate such phenomena in a large class of three dimensional superconformal field theories, known as the S-fold SCFTs. Supersymmetric indices are computed for a number of theories containing small rank gauge groups. It is found that indices of several models exhibit enhancement of supersymmetry at the superconformal fixed point in the infrared. Dualities between S-fold theories that have different quiver descriptions are also analysed. We explore a new class of theories with a discrete global symmetry, whose gauge symmetry in the quiver has a different global structure from those that have been studied earlier.
An S-fold has played an important role in constructing supersymmetric field theories with interesting features. It can be viewed as a type of AdS_4 solutions of Type IIB string theory where the fields in overlapping patches are glued by elements of SL(2,Z). This paper examines three dimensional quiver theories that arise from brane configurations with an inclusion of the S-fold. An important feature of such a quiver is that it contains a link, which is the T(U(N)) theory, between two U(N) groups, along with bifundamental and fundamental hypermultiplets. We systematically study the moduli spaces of those quiver theories, including the cases in which the non-zero Chern-Simons levels are turned on. A number of such moduli spaces turns out to have a very rich structure and tells us about the brane dynamics in the presence of an S-fold.
Magnetic quivers and Hasse diagrams for Higgs branches of rank 1 $4d$ $mathcal{N}=2$ SCFTs are provided. These rank 1 theories fit naturally into families of higher rank theories, originating from higher dimensions, which are addressed.
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