Factorization of Chiral String Amplitudes

TL;DR

This work investigates a chiral boundary-condition modification of closed-string theory, showing that flipping the spacetime metric in one open-string sector implements a simple operation on KLT-factorized amplitudes. In type II superstrings this leads to a complete truncation to massless states, reproducing pure supergravity amplitudes, while bosonic and heterotic strings display adjacent massive spin-2 states and tachyonic/ghost excitations arising from the flipped sector. The authors provide a derivation based on open-string decompositions and matrix factorization (F and S), and analyze three- and four-point amplitudes to reveal precise pole structures and residues under the flip. Overall, the paper demonstrates that chiral boundary conditions yield rational, highly constrained amplitudes and offers insights into the spectrum and potential field-theory interpretations, with implications for non-Hermitian formulations and duality-breaking scenarios.

Abstract

We re-examine a closed-string model defined by altering the boundary conditions for one handedness of two-dimensional propagators in otherwise-standard string theory. We evaluate the amplitudes using Kawai-Lewellen-Tye factorization into open-string amplitudes. The only modification to standard string theory is effectively that the spacetime Minkowski metric changes overall sign in one open-string factor. This cancels all but a finite number of states: As found in earlier approaches, with enough supersymmetry (e.g., type II) the tree amplitudes reproduce those of the massless truncation of ordinary string theory. However, we now find for the other cases that additional fields, formerly thought to be auxiliary, describe new spin-2 states at the two adjacent mass levels (tachyonic and tardyonic). The tachyon is always a ghost, but can be avoided in the heterotic case.