Elliptic modular double and 4d partition functions

Source abstract

Abstract We consider 4d supersymmetric (special) unitary Γ quiver gauge theories on compact manifolds which are T 2 fibrations over S 2 . We show that their partition functions are correlators of vertex operators and screening charges of the modular double version of elliptic W q , t ; q ′ ( Γ ) algebras. We also consider a generating function of BPS surface defects supported on T 2 and show that it can be identified with a particular coherent state in the Fock module over the elliptic Heisenberg algebra.