Beta functions of local fields of characteristic zero. Applications to string amplitudes

Abstract

For local fields of characteristic zero, along with the beta function we introduce a new sequence , , of beta functions of complex arguments expressed in terms of a product of gamma functions for arbitrary characters (ramified or not). We consider applications to the 4-particle tree string and superstring amplitudes. It turns out that the tachyon string amplitudes can be expressed in terms of the well-known beta function . The massless superstring amplitudes can be expressed in terms of the new beta function for non-trivial characters. We establish that the amplitudes of all known strings and superstrings admit adelic formulae.We give a new proof of the formula relating the 4-particle tree amplitudes for closed strings (generalized Virasoro amplitudes) to the product of two amplitudes for open strings (classical Veneziano amplitudes).