3d N $$ mathcal{N} $$ = 2 mirror symmetry, pq-webs and monopole superpotentials

D3 branes stretching between webs of (p,q) 5branes provide an interesting class of 3d $$ mathcal{n} $$ = 2 theories. for generic pq-webs however the low energy field theory is not known. we use 3d mirror symmetry and type iib s-duality to construct abelian gauge theories corresponding to d3 branes ending on both sides of a pq-web made of many coincident n s5’s intersecting one d5. these theories contain chiral monopole operators in the superpotential and enjoy a non trivial pattern of global symmetry enhancements. in the special case of the pq-web with one d5 and one n s5, the 3d low energy scft admits three dual formulations. this triality can be applied locally inside bigger quiver gauge theories. we prove our statements using partial mirror symmetry à la kapustin-strassler, showing the equality of the s 3 partition functions and studying the quantum chiral rings.