Analyticity of off-shell Green’s functions in superstring field theory

We consider the off-shell momentum space Green’s functions in closed superstring field theory. Recently in [1], the off-shell Green’s functions — after explicitly removing contributions of massless states — have been shown to be analytic on a domain (to be called the LES domain) in complex external momenta variables. Analyticity of off-shell Green’s functions in local QFTs without massless states in the primitive domain is a well-known result. Using complex Lorentz transformations and Bochner’s theorem allow to extend the LES domain to a larger subset of the primitive domain. For the 2-, 3- and 4-point functions, the full primitive domain is recovered. For the 5-point function, we are not able to obtain the full primitive domain analytically, only a large part of it is recovered. While this problem arises also for higher-point functions, it is expected to be only a technical issue.