A-twisted correlators and Hori dualities

Abstract

The Hori-Tong and Hori dualities are infrared dualities between two-dimensional gauge theories with $\mathcal{N}=(2,2)$ supersymmetry, which are reminiscent of four-dimensional Seiberg dualities. We provide additional evidence for those dualities with $U(N_c)$, $USp(2N_c)$, $SO(N)$ and $O(N)$ gauge groups, by matching correlation functions of Coulomb branch operators on a Riemann surface ${\Sigma }_g$, in the presence of the topological $A$-twist. The $O(N)$ theories studied, denoted by $O_{+}(N)$ and $O_{-}(N)$, can be understood as ${\mathbb{Z}}_2$ orbifolds of an $SO(N)$ theory. The correlators of these theories on ${\Sigma }_g$ with $g>0$ are obtained by computing correlators with ${\mathbb{Z}}_2$-twisted boundary conditions and summing them up with weights determined by the orbifold projection.

arXiv comment45 pages plus appendix; v2: updated bibliography and acknowledgements

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• Notes on two-dimensional pure supersymmetric gauge theories
• Quantum Sheaf Cohomology and Duality of Flag Manifolds
• Branes and 2d N=(2,2) gauge theories with orthogonal and symplectic groups
• Supersymmetric Wilson loops in two dimensions and duality
• Superconformal indices, Seiberg dualities and special functions
• Testing the (0,2) mirror map
• Correlation functions in massive Landau-Ginzburg orbifolds and tests of dualities
• 2d duality for orthogonal gauge theories with 8 supersymmetries
• 2D Seiberg-like dualities for orthogonal gauge groups