Little string instanton partition functions and scalar propagators

bstract We discuss a class of Little String Theories (LSTs) whose low energy descriptions are supersymmetric gauge theories on the Ω-background with gauge group U( N ) and matter in the adjoint representation. We show that the instanton partition function of these theories can be written in terms of Kronecker-Eisenstein series, which in a particular limit of the deformation parameters of the Ω-background organise themselves into Greens functions of free scalar fields on a torus. We provide a concrete identification between (differences of) such propagators and Nekrasov subfunctions. The latter are also characterised by counting specific holomorphic curves in a Calabi-Yau threefold X N, 1 which engineers the LST. Furthermore, using the formulation of the partition function in terms of the Kronecker-Eisenstein series, we argue for new recursive structures which relate higher instanton contributions to products of lower ones.