The complex null string, Galilean conformal algebra and scattering equations

Abstract

The scattering equation formalism for scattering amplitudes, and its stringy incarnation, the ambitwistor string, remains a mysterious construction. In this paper, we pursue the study a gauged-unfixed version of the ambitwistor string known as the null string. We explore the following three aspects in detail; its complexification, gauge fixing, and amplitudes. We first study the complexification of the string; the associated symmetries and moduli, and connection to the ambitwistor string. We then look in more details at the leftover symmetry algebra of the string, called Galilean conformal algebra; we study its local and global action and gauge-fixing. We finish by presenting an operator formalism, that we use to compute tree-level scattering amplitudes based on the scattering equations and a one-loop partition function. These results hopefully will open the way to understand conceptual questions related to the loop expansion in these twistor-like string models.

References added

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• Plane wave backgrounds and colour-kinematics duality
• Carroll covariant scalar fields in two dimensions
• Boosting to BMS
• Inhomogeneous Tensionless Superstrings
• Amplitudes on plane waves from ambitwistor strings
• A String Theory Which Isn't About Strings
• On integrands and loop momentum in string and field theory
• Integrable systems with BMS${}_3$ Poisson structure and the dynamics of locally flat spacetimes
• BMS Characters and Modular Invariance
• Windings of twisted strings
• The Shadow Formalism of Galilean CFT${}_2$
• Bosonic sectorized strings and the $(DF{)}^2$ theory
• Spinor frame formalism for amplitudes and constrained superamplitudes of 10D SYM and 11D supergravity
• An analytic superfield formalism for tree superamplitudes in D=10 and D=11
• BMS Modular Diaries: Torus one-point function
• Chiral strings, the sectorized description and their integrated vertex operators
• On polarized scattering equations for superamplitudes of 11D supergravity and ambitwistor superstring
• Tensionless Tales: Vacua and Critical Dimensions