Graviton and Massive Symmetric Rank-two Tensor in String Theory

Abstract

Spin-two particles appear in the spectra of both open and closed string theories. We studied a graviton and massive symmetric rank-two tensor in string theory, both of which carry spin two. A graviton is a massless spin-two particle in closed string theory while a symmetric rank-two tensor is a massive particle with spin two in open string theory. Using Polyakov's string path integral formulation of string scattering amplitudes, we calculated cubic interactions of both spin-two particles explicitly, including $\ap$-corrections (string corrections). We observed that the cubic interactions of the massive spin-two particle differed from those of the graviton. The massive symmetric rank-two tensor in open string theory becomes massless in the high energy limit where $\ap \rightarrow \infty$ and $\ap$-correction terms, containing higher derivatives, dominate: In this limit the local cubic action of the symmetric rank-two tensor of open string theory coincides with that of the graviton in closed string theory.