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 λ. Under these new boundary conditions, the left-moving and right-moving modes are treated unequally. Thus, we called them chiral string theories. If λ = −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 λ. 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 λ = ±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.