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We discuss a class of Little String Theories (LSTs) whose low energydescriptions are supersymmetric gauge theories on the $\Omega$-background withgauge group $U(N)$ and matter in the adjoint representation. We show that theinstanton partition function of these theories can be written in terms ofKronecker-Eisenstein series, which in a particular limit of the deformationparameters of the $\Omega$-background organise themselves into Greens functionsof free scalar fields on a torus. We provide a concrete identification between(differences of) such propagators and Nekrasov subfunctions. The latter arealso characterised by counting specific holomorphic curves in a Calabi-Yauthreefold $X_{N,1}$ which engineers the LST. Furthermore, using the formulationof the partition function in terms of the Kronecker-Eisenstein series, we arguefor new recursive structures which relate higher instanton contributions toproducts of lower ones.

Little String Instanton Partition Functions and Scalar Propagators