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

Abstract

D3 branes stretching between webs of (p,q) 5branes provide an interesting class of 3d 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 symmetryà la Kapustin-Strassler, showing the equality of the S 3 b partition functions and studying the quantum chiral rings.

Mirror theories of 3d $$ \mathcal{N} $$ = 2 SQCD

“…This was achieved with a variety of arguments including stringy-inspired constructions [3][4][5][6][7][8][9]. One natural question is then whether this family of dualities can be extended to more general 3d N = 2 theories.…”

USp(2Nc) SQCD3 with antisymmetric: dualities and symmetry enhancements

“…See also[17,[24][25][26][27] for other applications of monopole superpotentials to 3d N = 2 theories.…”

q-Virasoro Modular Double and 3d Partition Functions

“…First of all, the W q,t modular double symmetry of 3d N = 2 quiver gauge theories on compact spaces that we have considered represents a new tool for studying these theories, which should supplement the existing large N [130,131] or Fermi gas techniques [132][133][134][135]. Moreover, it is very likely that the 3d dualities mentioned in the introduction (see also [136] for recent new results) have a natural and simple interpretation in W q,t language, perhaps along the lines of [137] in the more familiar 4d AGT context. It is also interesting to observe the appearance of W-like symmetries in these theories, which are usually associated to area-preserving diffeomorphisms of membranes (a possible connection between W q,t algebras and the physics of membranes was already pointed out in [109]).…”