Ambitwistor strings and the scattering equations at one loop

TL;DR

This work extends ambitwistor string theory beyond genus-zero by incorporating Ramond-sector fermions and formulating genus-one scattering equations for NS-NS states, thereby proposing new representations for one-loop supergravity amplitudes. It establishes modular invariance of the ambitwistor string partition function, derives explicit genus-one NS-NS amplitudes as Pfaffian expressions, and verifies correct factorization behavior in both non-separating and separating degenerations. The results illuminate how a chiral, massless spectrum string can reproduce field-theory-like loop integrands while maintaining a worldsheet framework localized to scattering-equation solutions. The study also discusses limitations and future directions, including the potential of pure spinor formalisms and connections to KLT-like relations at higher genus.

Abstract

Ambitwistor strings are chiral, infinite tension analogues of conventional string theory whose target space is the space of complex null geodesics and whose spectrum consists exclusively of massless states. At genus zero, these strings underpin the Cachazo-He-Yuan formulae for tree level scattering of gravitons, gluons and scalars. In this paper we extend these formulae in a number of directions. Firstly, we consider Ramond sector vertex operators and construct simple amplitudes involving space-time fermions. These agree with tree amplitudes in ten dimensional supergravity and super Yang--Mills. We then show that, after the usual GSO projections, the ambitwistor string partition function is modular invariant. We consider the scattering equations at genus one, and calculate one loop scattering amplitudes for NS-NS external states in the Type II ambitwistor string. We conjecture that these give new representations of (the integrand of) one loop supergravity amplitudes and we show that they have the expected behaviour under factorization of the worldsheet in both non--separating and separating degenerations.