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We propose confining dualities of $\mathcal{N}=(0,2)$ half-BPS boundaryconditions in 3d $\mathcal{N}=2$ 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 haveNeumann boundary conditions. While some of the dualities can be extended to 3dbulk dualities, others should be understood intrinsically as 2d dualities asthey seem to hold only at the boundary. The gauge theory Neumann half-indicesare well-defined even for theories which contain monopole operators withnon-positive scaling dimensions and they are given by Askey-Wilson type$q$-beta integrals. As a consequence of the confining dualities, newconjectural identities of such integrals are found.

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