Orthosymplectic Quivers: Indices, Hilbert Series, and Generalised Symmetries
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arXiv
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| Natura: | Preprint |
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2025
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| _version_ | 1866910066843582464 |
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| author | Harding, William Mekareeya, Noppadol Zhong, Zhenghao |
| author_facet | Harding, William Mekareeya, Noppadol Zhong, Zhenghao |
| contents | We investigate generalised global symmetries in 3d $\mathcal{N}=4$ orthosymplectic quiver gauge theories. Using the superconformal index, we identify a $D_8$ categorical symmetry web in a class of theories featuring $\mathfrak{so}(2N) \times \mathfrak{usp}(2N)$ gauge algebra (at zero Chern-Simons levels) and $n$ bifundamental half-hypermultiplets, analogous to ABJ-type models. As a distinct contribution, we improve the prescription, previously studied in the literature, for computing Coulomb branch Hilbert series of $\mathrm{SO}(N)$ gauge theories with $N_f$ vector hypermultiplets. Our improved prescription extends these methods by incorporating fugacities for discrete zero-form symmetries - specifically charge conjugation and magnetic symmetries - and properly treating background magnetic fluxes for the flavour symmetry. This refinement enables calculations for various global forms ($\mathrm{O}(N)^\pm, \mathrm{Spin}(N), \mathrm{Pin}(N)$) and ensures consistency with the Coulomb branch limit of the superconformal index and known dualities. The proper treatment of fluxes is particularly essential for analysing orthosymplectic quivers where such a flavour symmetry is gauged. We verify our methods through several examples, including an analysis of the mapping of discrete symmetries under mirror symmetry for $T[\mathrm{SO}(N)]$ and $T[\mathrm{USp}(2N)]$ theories. The analysis also readily generalises to the $T_ρ[\mathrm{SO}(N)]$ and $T_ρ[\mathrm{USp}(2N)]$ theories associated with partition $ρ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03875 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Orthosymplectic Quivers: Indices, Hilbert Series, and Generalised Symmetries Harding, William Mekareeya, Noppadol Zhong, Zhenghao High Energy Physics - Theory We investigate generalised global symmetries in 3d $\mathcal{N}=4$ orthosymplectic quiver gauge theories. Using the superconformal index, we identify a $D_8$ categorical symmetry web in a class of theories featuring $\mathfrak{so}(2N) \times \mathfrak{usp}(2N)$ gauge algebra (at zero Chern-Simons levels) and $n$ bifundamental half-hypermultiplets, analogous to ABJ-type models. As a distinct contribution, we improve the prescription, previously studied in the literature, for computing Coulomb branch Hilbert series of $\mathrm{SO}(N)$ gauge theories with $N_f$ vector hypermultiplets. Our improved prescription extends these methods by incorporating fugacities for discrete zero-form symmetries - specifically charge conjugation and magnetic symmetries - and properly treating background magnetic fluxes for the flavour symmetry. This refinement enables calculations for various global forms ($\mathrm{O}(N)^\pm, \mathrm{Spin}(N), \mathrm{Pin}(N)$) and ensures consistency with the Coulomb branch limit of the superconformal index and known dualities. The proper treatment of fluxes is particularly essential for analysing orthosymplectic quivers where such a flavour symmetry is gauged. We verify our methods through several examples, including an analysis of the mapping of discrete symmetries under mirror symmetry for $T[\mathrm{SO}(N)]$ and $T[\mathrm{USp}(2N)]$ theories. The analysis also readily generalises to the $T_ρ[\mathrm{SO}(N)]$ and $T_ρ[\mathrm{USp}(2N)]$ theories associated with partition $ρ$. |
| title | Orthosymplectic Quivers: Indices, Hilbert Series, and Generalised Symmetries |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2505.03875 |