Web of Seiberg-like dualities for 3D N = 2 quivers

We study the topologically twisted index of 3d $$ \mathcal{N} $$ N = 2 supersymmetric gauge theories with unitary gauge groups. We implement a Gröbner basis algorithm for computing the Σg× S1 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(Nc)k,k+lNc with l ≠ 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 ≠ 0.

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

Closset

Khlaif

2023

Line defect half-indices of SU(N) Chern-Simons theories

Okazaki,

Smith

2024

We study the Wilson line defect half-indices of 3d $$ \mathcal{N} $$ N = 2 supersymmetric SU(N) Chern-Simons theories of level k ≤ – N with Neumann boundary conditions for the gauge fields, together with 2d Fermi multiplets and fundamental 3d chiral multiplets to cancel the gauge anomaly. We derive some exact results and also make some conjectures based on expansions of the q-series. We find several interesting connections with special functions known in the literature, including Rogers-Ramanujan functions for which we conjecture integral representations, and the appearance of Appell-Lerch sums for certain Wilson line half-index grand canonical ensembles which reveal an unexpected appearance of mock modular functions. We also find intriguing q-difference equations relating half-indices to Wilson line half-indices. Some of these results also have a description in terms of a dual theory with Dirichlet boundary conditions for the vector multiplet in the dual theory.

Boundary confining dualities and Askey-Wilson type q-beta integrals

Okazaki

Smith

2023

Self Cite

We propose confining dualities of $$ \mathcal{N} $$ N = (0, 2) half-BPS boundary conditions in 3d $$ \mathcal{N} $$ N = 2 supersymmetric SU(N), USp(2n) and SO(N) gauge theories. Some of these dualities have the novel feature that one (anti)fundamental chiral has Dirichlet boundary condition while the rest have Neumann boundary conditions. While some of the dualities can be extended to 3d bulk dualities, others should be understood intrinsically as 2d dualities as they seem to hold only at the boundary. The gauge theory Neumann half-indices are well-defined even for theories which contain monopole operators with non-positive scaling dimensions and they are given by Askey-Wilson type q-beta integrals. As a consequence of the confining dualities, new conjectural identities of such integrals are found.