Chiral string theories as an interpolation between strings and particles

A new set of boundary conditions for string propagators is proposed in this paper. The boundary conditions are parametrized by a complex number $\lambda$. Under these new boundary conditions, the left-moving and right-moving modes are treated unequally. Thus, we called them chiral string theories. If $\lambda = -1$, the spectrum of such theory truncates to a finite number, and therefore it becomes a different description of supergravity. We found the spectrum of chiral string theories by requiring that the vertex operators are conformally invariant. In addition, we also calculate the amplitudes for arbitrary $\lambda$. The amplitudes are expressed as a product of open string amplitudes which are similar to the KLT relation. The unitarity of these theories are investigated. However, we found out that except for $\lambda = \pm 1$, all other theories are not unitary; i.e., only the supergravity and ordinary strings are unitary. Although most of the chiral strings are not physical, they still serve as a valuable tool in studying the relation between particle theories and string theories.