Abstract
We show that not all (2 + 1) dimensional toric phases are Seiberg-like duals. Particularly, we work out superconformal indices for the toric phases of Fanos \( {\mathcal{C}}_3 \), \( {\mathcal{C}}_5 \) and \( {\mathrm{\mathcal{B}}}_2 \). We find that the indices for the two toric phases of Fano \( {\mathrm{\mathcal{B}}}_2 \) do not match, which implies that they are not Seiberg-like duals. We also take the route of acting Seiberg-like duality transformation on toric quiver Chern-Simons theories to obtain dual quivers. We study two examples and show that Seiberg-like dual quivers are not always toric quivers.
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Dwivedi, S., Ramadevi, P. Is toric duality a Seiberg-like duality in (2 + 1)-d ?. J. High Energ. Phys. 2014, 84 (2014). https://doi.org/10.1007/JHEP07(2014)084
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DOI: https://doi.org/10.1007/JHEP07(2014)084