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Register a new userQuiver origami: discrete gauging and folding
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We study two types of discrete operations on Coulomb branches of $3d$ $mathcal{N}=4$ quiver gauge theories using both abelianisation and the monopole formula. We generalise previous work on discrete quotients of Coulomb branches and introduce novel wreathed quiver theories. We further study quiver folding which produces Coulomb branches of non-simply laced quivers.
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We analyse the Higgs branch of 4d $mathcal{N}=2$ SQCD gauge theories with non-connected gauge groups $widetilde{mathrm{SU}}(N) = mathrm{SU}(N) rtimes_{I,II} mathbb{Z}_2$ whose study was initiated in arXiv:1804.01108. We derive the Hasse diagrams corresponding to the Higgs mechanism using adapted characters for representations of non-connected groups. We propose 3d $mathcal{N}=4$ magnetic quivers for the Higgs branches in the type $I$ discrete gauging case, in the form of recently introduced wreathed quivers, and provide extensive checks by means of Coulomb branch Hilbert series computations.
In this note, using Nekrasovs gauge origami framework, we study two differe
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 $SL(2,mathbb{Z})$ 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 Coloumb 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.
This paper tests a conjecture on discrete non-Abelian gauging of 3d $mathcal{N} = 4$ supersymmetric quiver gauge theories. Given a parent quiver with a bouquet of $n$ nodes of rank $1$, invariant under a discrete $S_n$ global symmetry, one can construct a daughter quiver where the bouquet is substituted by a single adjoint $n$ node. Based on the main conjecture in this paper, the daughter quiver corresponds to a theory where the $S_n$ discrete global symmetry is gauged and the new Coulomb branch is a non-Abelian orbifold of the parent Coulomb branch. We demonstrate and test the conjecture for three simply laced families of bouquet quivers and a non-simply laced bouquet quiver with $C_2$ factor in the global symmetry.
Rigid origami, with applications ranging from nano-robots to unfolding solar sails in space, describes when a material is folded along straight crease line segments while keeping the regions between the creases planar. Prior work has found explicit equations for the folding angles of a flat-foldable degree-4 origami vertex. We extend this work to generalized symmetries of the degree-6 vertex where all sector angles equal $60^circ$. We enumerate the different viable rigid folding modes of these degree-6 crease patterns and then use $2^{nd}$-order Taylor expansions and prior rigid folding techniques to find algebraic folding angle relationships between the creases. This allows us to explicitly compute the configuration space of these degree-6 vertices, and in the process we uncover new explanations for the effectiveness of Weierstrass substitutions in modeling rigid origami. These results expand the toolbox of rigid origami mechanisms that engineers and materials scientists may use in origami-inspired designs.
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