Chiral Superstring and CHY Amplitude

TL;DR

This work analyzes gauge choices in chiral string theories and shows how HSZ singular gauge limits, applied before bar-z integration, localize amplitudes to CHY-like structures. Using the pure spinor formalism for heterotic strings, the authors demonstrate that the bosonic sector reproduces CHY Yang-Mills amplitudes while the fermionic sector yields the supersymmetric CHY generalization, with boundary conditions playing a crucial role in ensuring gauge independence. They establish BRST-equivalence with the Mason–Skinner ambitwistor framework (MS prescription) and outline a practical route to N-point and loop amplitudes via singular gauge limits. The results connect CHY formulations to traditional string-theoretic calculations, offering a BRST-consistent, gauge-invariant route to SUSY CHY amplitudes and their gravitational counterparts.

Abstract

We calculate the chiral string amplitude in pure spinor formalism and take four point amplitude as an example. The method could be easily generalized to $N$ point amplitude by complicated calculations. By doing the usual calculations of string theory first and using a special singular gauge limit, we produce the amplitude with the integral over Dirac $δ$-functions. The Bosonic part of the amplitude matches the CHY amplitude and the Fermionic part gives us the supersymmetric generalization of CHY amplitude. Finally, we also check the dependence on boundary condition for heterotic chiral string amplitudes.