T-duality and Scattering of Stringy States

Abstract: We present a procedure for application of T-duality transformation on scattering amplitudes of closed bosonic stringy states. These states arise due to compactification of closed string to lower spacetime dimensions through dimensional reduction. The amplitude, in the first quantized formalism, is computed by introducing vertex operators. The amplitude is constructed by the standard prescription and the vertex operators are required to respect conformal invariance. Such vertex operators are constructed in the weak field approximation. Therefore, the vertex operators of the stringy states of our interest are to be defined accordingly. We propose a prescription to implement T-duality on the three point functions and N-point functions. We argue that it is possible to generate new amplitudes through the transformations on a given amplitude just as T-duality transformations can take us to a new set of string vacuum when acted upon an initial set. Explicit examples are given for three point and four point functions.