Abstract
We compute the 3d mathcal{N} = 2 superconformal indices for 3d/1d coupled systems, which arise as the worldvolume theories of intersecting surface defects engineered by Higgsing 5d mathcal{N} = 1 gauge theories. We generalize some known 3d dualities, including non-Abelian 3d mirror symmetry and 3d/3d correspondence, to some of the simple 3d/1d coupled systems. Finally we propose a q-Virasoro construction for the superconformal indices.
Highlights
We compute the 3d N = 2 superconformal indices for 3d/1d coupled systems, which arise as the worldvolume theories of intersecting surface defects engineered by Higgsing 5d N = 1 gauge theories
That will couple to the bulk theory in such a way that a certain amount of supersymmetry is preserved
We report an equality at the level of D2 × S1 partition function of a simplest theory of intersecting SQEDs and a matrix integral, which could be a generalization to the known duality
Summary
Consider a theory T with a flavor symmetry subgroup SU(N ). At these values, the poles of the following form, coming from the fundamental hypermultiplet one-loop contributions, of the integrand pinch the contour since there are only N − 1 independent variables zA, bμιA p−nLA. The residue can be extracted by performing a contour integral of b, which effectively gauges U(1) flavor symmetry and making the SU(N ) theory into a U(N ) theory. One can further pull away the NS5 brane from the web while stretching nL D3L and nR D3R branes which extend in different directions as shown in the above table These D3-branes support the worldvolume theories of the codimension-two defects in the bulk 5d theory. The S-duality of the (p, q)-web leaves the partition function invariant, which is associated to identities involving the (skew-) Macdonald polynomials [74]
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