Chiral Closed strings: Four massless states scattering amplitude

TL;DR

This work computes four-point scattering amplitudes of massless states for closed chiral strings (bosonic, Type II, and heterotic) using KLT factorization, demonstrating that the amplitudes factorize into products of cubic amplitudes with intermediate states. For Type II, only massless gravitational intermediates contribute, yielding a manifestly $stu$-symmetric amplitude free of tachyonic poles, while the bosonic chiral string also features tachyon and tardyon poles whose residues enforce a traceless intermediate spin-2 state and reveal ghost-like behavior, fixing the critical dimension to $D=26$. The authors verify the equivalence between the KLT amplitude and the product of two three-point amplitudes across channels, including a careful treatment of massive intermediates via projection operators. In the heterotic case, the massless sector admits the same factorization approach, illustrating the broader applicability of the method and highlighting the field-theory-like structure of these string amplitudes and their potential implications for low-energy effective actions and massive gravity-type interpretations.

Abstract

We compute the scattering amplitudes of four massless states for chiral (closed) bosonic and type II superstrings using the Kawai-Lewellen-Tye ($KLT$) factorization method. The amplitude in the chiral bosonic case is identical to a field theory amplitude corresponding to the spin-$2$ tachyon, massless gravitational sector and massive spin-2 tardyon states of the spectrum. Chiral type II superstrings amplitude only possess poles associated with the massless gravitational sector. We briefly discuss the extension of the calculation to heterotic superstrings.