Twisted indices, Bethe ideals and 3d N=2 infrared dualities

We study the topologically twisted index of 3d N = 2 supersymmetric gauge theories with unitary gauge groups. We implement a Grobner basis algorithm for computing the Sigma(g) x S-1 index explicitly and exactly in terms of the associated Bethe ideal, which is defined as the algebraic ideal associated with the Bethe equations of the corresponding 3d A-model. We then revisit recently discovered infrared dualities for unitary SQCD with gauge group U( N-c) (k,k+ lNc) with l not equal 0, namely the Nii duality that generalises the Giveon-Kutasov duality, the Amariti-Rota duality that generalises the Aharony duality, and their further generalisations in the case of arbitrary numbers of fundamental and antifundamental chiral multiplets. In particular, we determine all the flavour Chern-Simons contact terms needed to make these dualities work. This allows us to check that the twisted indices of dual theories match exactly. We also initiate the study of the Witten index of unitary SQCD with l 6= 0.

Automated summary

In this study, we investigate the relationship between the topologically twisted index and unitary gauge groups in 3d N=2 supersymmetric gauge theories. We use a Grobner basis algorithm to calculate the Sigma(g) x S-1 index explicitly and exactly, in terms of the associated Bethe ideal. We also examine the recently discovered infrared dualities for unitary SQCD and determine the necessary flavor Chern-Simons contact terms. Additionally, we initiate the study of the Witten index for unitary SQCD with l≠0.