Satoshi Nawata, Marcus Sperling, Hao Ellery Wang, Zhenghao Zhong
SciPost Phys. 15, 033 (2023) ·
published 27 July 2023

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The study of 3d mirror symmetry has greatly enhanced our understanding of various aspects of 3d $\mathcal{N}=4$ theories. In this paper, starting with known mirror pairs of 3d $\mathcal{N}=4$ quiver gauge theories and gauging discrete subgroups of the flavour or topological symmetry, we construct new mirror pairs with nontrivial 1form symmetry. By providing explicit quiver descriptions of these theories, we thoroughly specify their symmetries (0form, 1form, and 2group) and the mirror maps between them.
SciPost Phys. 14, 034 (2023) ·
published 15 March 2023

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The rational $Q$system is an efficient method to solve Bethe ansatz equations for quantum integrable spin chains. We construct the rational $Q$systems for generic Bethe ansatz equations described by an $A_{\ell1}$ quiver, which include models with multiple momentum carrying nodes, generic inhomogeneities, generic diagonal twists and $q$deformation. The rational $Q$system thus constructed is specified by two partitions. Under Bethe/Gauge correspondence, the rational $Q$system is in a onetoone correspondence with a 3d $\mathcal{N}=4$ quiver gauge theory of the type ${T}_{{\rho}}^{{\sigma}}[\mathrm{SU}(n)]$, which is also specified by the same partitions. This shows that the rational $Q$system is a natural language for the Bethe/Gauge correspondence, because known features of the ${T}_{{\rho}}^{{\sigma}}[\mathrm{SU}(n)]$ theories readily translate. For instance, we show that the Higgs and Coulomb branch Higgsing correspond to modifying one of the partitions in the rational $Q$system while keeping the other untouched. Similarly, mirror symmetry is realized in terms of the rational $Q$system by simply swapping the two partitions  exactly as for ${T}_{{\rho}}^{{\sigma}}[\mathrm{SU}(n)]$. We exemplify the computational efficiency of the rational $Q$system by evaluating topologically twisted indices for 3d $\mathcal{N}=4$ $\mathrm{U}(n)$ SQCD theories with $n=1,\ldots,5$.
Dr Sperling: "We are grateful to the referee..."
in Submissions  report on 3d $\mathcal{N}=4$ mirror symmetry with 1form symmetry