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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.
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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.
We explore the geometrical structure of Higgs branches of quantum field theories with 8 supercharges in 3, 4, 5 and 6 dimensions. They are symplectic singularities, and as such admit a decomposition (or foliation) into so-called symplectic leaves, which are related to each other by transverse slices. We identify this foliation with the pattern of partial Higgs mechanism of the theory and, using brane systems and recently introduced notions of magnetic quivers and quiver subtraction, we formalise the rules to obtain the Hasse diagram which encodes the structure of the foliation. While the unbroken gauge symmetry and the number of flat directions are obtainable by classical field theory analysis for Lagrangian theories, our approach allows us to characterise the geometry of the Higgs branch by a Hasse diagram with symplectic leaves and transverse slices, thus refining the analysis and extending it to non-Lagrangian theories. Most of the Hasse diagrams we obtain extend beyond the cases of nilpotent orbit closures known in the mathematics literature. The geometric analysis developed in this paper is applied to Higgs branches of several Lagrangian gauge theories, Argyres-Douglas theories, five dimensional SQCD theories at the conformal fixed point, and six dimensional SCFTs.
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.
We present a comparative study of inflation in two theories of quadratic gravity with {it gauged} scale symmetry: 1) the original Weyl quadratic gravity and 2) the theory defined by a similar action but in the Palatini approach obtained by replacing the Weyl connection by its Palatini counterpart. These theories have different vectorial non-metricity induced by the gauge field ($w_mu$) of this symmetry. Both theories have a novel spontaneous breaking of gauged scale symmetry, in the absence of matter, where the necessary scalar field is not added ad-hoc to this purpose but is of geometric origin and part of the quadratic action. The Einstein-Proca action (of $w_mu$), Planck scale and metricity emerge in the broken phase after $w_mu$ acquires mass (Stueckelberg mechanism), then decouples. In the presence of matter ($phi_1$), non-minimally coupled, the scalar potential is similar in both theories up to couplings and field rescaling. For small field values the potential is Higgs-like while for large fields inflation is possible. Due to their $R^2$ term, both theories have a small tensor-to-scalar ratio ($rsim 10^{-3}$), larger in Palatini case. For a fixed spectral index $n_s$, reducing the non-minimal coupling ($xi_1$) increases $r$ which in Weyl theory is bounded from above by that of Starobinsky inflation. For a small enough $xi_1leq 10^{-3}$, unlike the Palatini version, Weyl theory gives a dependence $r(n_s)$ similar to that in Starobinsky inflation, while also protecting $r$ against higher dimensional operators corrections.
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