Worldsheet Geometries of Ambitwistor String

TL;DR

This work develops a geometric, BRST-consistent framework for ambitwistor-string amplitudes by treating the amplitude measure as a holomorphic top-form on the cotangent bundle of the moduli space and using Morse-theory–defined integration cycles to localize to scattering-equation solutions. It extends the bosonic construction to a family of fermionic chiral CFTs with up to four worldsheet fermions, detailing the BRST structure, vertex operators, holomorphic forms on supersymmetric bundles, and localization/ factorization properties. The analysis reveals how physical propagators emerge after appropriate GSO-type projections and identifies potential avenues to realize theories like DBI and Galileon via $N=3$ and $N=4$ ambitwistor strings. Overall, the paper provides a comprehensive worldsheet-geometric formulation of ambitwistor amplitudes, clarifies the treatment of delta-forms and cycles, and points to rich future directions in internal CFT building blocks and loop rationality. It thus strengthens the link between CHY-type amplitudes and a two-dimensional chiral CFT description of massless theories, with implications for both foundational understanding and potential new theories derived from ambitwistor strings.

Abstract

Mason and Skinner proposed the ambitwistor string theory which directly reproduces the formulas for the amplitudes of massless particles proposed by Cachazo, He and Yuan. In this paper we discuss geometries of the moduli space of worldsheets associated to the bosonic or the RNS ambitwistor string. Further, we investigate the factorization properties of the amplitudes when an internal momentum is near on-shell in the abstract CFT language. Along the way, we propose the existence of the ambitwistor strings with three or four fermionic worldsheet currents.