Elliptic modular double and 4d partition functions

Authors: Rebecca Lodin, Fabrizio Nieri, Maxim Zabzine Preprint number: UUITP-09/17 We consider 4d supersymmetric (special) unitary  quiver gauge theories on compact manifolds which are  fibrations over . We show that their partition functions are correlators of vertex operators and screening charges of the modular double version of elliptic  algebras. We also consider a generating function of BPS surface defects supported on  and show that it can be identified with a particular coherent state in the Fock module over the elliptic Heisenberg algebra.