We study partition functions of 3d N= 2 U (N) gauge theories on compact manifolds which are S1 fibrations over S2. We show that the partition functions are free field correlators of vertex operators and screening charges of the q-Virasoro modular double, which we define. The inclusion of supersymmetric Wilson loops in arbitrary representations allows us to show that the generating functions of Wilson loop vacuum expectation values satisfy two SL (2 , Z) -related commuting sets of q-Virasoro constraints. We generalize our construction to 3d N= 2 unitary quiver gauge theories and as an example we give the free boson realization of the ABJ(M) model.
q-Virasoro Modular Double and 3d Partition Functions
Nieri F.;
2017-01-01
Abstract
We study partition functions of 3d N= 2 U (N) gauge theories on compact manifolds which are S1 fibrations over S2. We show that the partition functions are free field correlators of vertex operators and screening charges of the q-Virasoro modular double, which we define. The inclusion of supersymmetric Wilson loops in arbitrary representations allows us to show that the generating functions of Wilson loop vacuum expectation values satisfy two SL (2 , Z) -related commuting sets of q-Virasoro constraints. We generalize our construction to 3d N= 2 unitary quiver gauge theories and as an example we give the free boson realization of the ABJ(M) model.
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