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Rational $Q$-systems, Higgsing and Mirror Symmetry
- Source :
- SciPost Phys. 14, 034 (2023)
- Publication Year :
- 2022
-
Abstract
- 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 $A_{\ell-1}$ 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 one-to-one correspondence with a 3d $\mathcal{N}=4$ quiver gauge theory of the type ${T}_{\boldsymbol{\rho}}^{\boldsymbol{\sigma}}[SU(n)]$, 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 ${T}_{\boldsymbol{\rho}}^{\boldsymbol{\sigma}}[SU(n)]$ 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 ${T}_{\boldsymbol{\rho}}^{\boldsymbol{\sigma}}[SU(n)]$. We exemplify the computational efficiency of the rational $Q$-system by evaluating topologically twisted indices for 3d $\mathcal{N}=4$ $U(n)$ SQCD theories with $n=1,\ldots,5$.<br />Comment: v3: 53 pages + appendices, added clarifications, fixed typos
- Subjects :
- High Energy Physics - Theory
Subjects
Details
- Database :
- arXiv
- Journal :
- SciPost Phys. 14, 034 (2023)
- Publication Type :
- Report
- Accession number :
- edsarx.2208.10047
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.21468/SciPostPhys.14.3.034