Twisted indices, Bethe ideals and 3d $$ \mathcal{N} $$ = 2 infrared dualities

A bstract We study the topologically twisted index of 3d $$ \mathcal{N} N = 2 supersymmetric gauge theories with unitary groups. implement a Gröbner basis algorithm for computing Σ g × S 1 explicitly and exactly in terms associated Bethe ideal, which is defined as algebraic ideal equations corresponding -model. then revisit recently discovered infrared dualities SQCD group U( N c ) k,k + lNc l ≠ 0, namely Nii duality that generalises Giveon-Kutasov duality, Amariti-Rota Aharony their further generalisations case arbitrary numbers fundamental antifundamental chiral multiplets. In particular, we determine all flavour Chern-Simons contact needed to make these work. This allows us check indices dual match exactly. also initiate Witten 0.