Field theory expansions of string theory amplitudes

It is commonly believed that string theory amplitudes cannot be expanded in terms of poles of all channels, thereby distinguishing them from the usual Feynman diagram expansion in quantum field theory. We present here new representations of the Euler-Beta function and string theory amplitudes which are analytic everywhere except at the poles but sum over poles in all channels, and, crucially, include contact diagrams, very much in the spirit of quantum field theory. This enables us to consider mass-level truncation, which preserves all the features of the original amplitude. By starting with such expansions for generalized Euler-Beta functions and demanding QFT like features, we single out the open string amplitude. Our considerations also lead to new field theory inspired representations of the Zeta function, which have very fast convergence. We demonstrate the difficulty in deforming away from the string amplitude and show that a class of such deformations can be potentially interesting when there is level truncation.