P-Adic string theories

Abstract

In this paper we study the p-adic string theory. Starting with the integral representation of the real string scattering amplitude, we obtain various p-adic string amplitudes. We show that it is possible to obtain a suitable p-adic theory starting with either the Koba-Nielsen or the Bardakçi-Ruegg formula. However, whereas in the real string case both representations of the amplitude correspond to the same theory, the p-adic generalizations lead to different theories. Furthermore, there is more than one p-adic generalization of each form of the amplitude. Each p-adic theory gives its own set of diagrammatic rules implying that it is describable by some nonlocal effective field theory. For completeness, in the first part of the paper we give an overview of the p-adic mathematics necessary for constructing our generalizations and for computing the resultant p-adic amplitudes.