New Worldsheet Formulae for Conformal Supergravity Amplitudes

TL;DR

This paper derives new worldsheet formulae for tree-level conformal supergravity amplitudes using 4d ambitwistor string theory, providing concise, supersymmetric expressions supported on refined scattering equations, and introduces a method for computing momentum derivatives of spinor variables.

Contribution

It presents the first concise worldsheet formulae for conformal supergravity amplitudes supported on refined scattering equations, including a supersymmetric extension and a method for momentum derivatives.

Findings

Derived worldsheet formulae for conformal supergravity amplitudes.

Formulated a method for momentum derivatives of spinor variables.

Extended the framework to include non-plane wave boundary conditions.

Abstract

We use 4d ambitwistor string theory to derive new worldsheet formulae for tree-level conformal supergravity amplitudes supported on refined scattering equations. Unlike the worldsheet formulae for super-Yang-Mills or supergravity, the scattering equations for conformal supergravity are not in general refined by MHV degree. Nevertheless, we obtain a concise worldsheet formula for any number of scalars and gravitons which we lift to a manifestly supersymmetric formula using four types of vertex operators. The theory also contains states with non-plane wave boundary conditions and we show that the corresponding amplitudes can be obtained from plane-wave amplitudes by applying momentum derivatives. Such derivatives are subtle to define since the formulae are intrinsically four-dimensional and on-shell, so we develop a method for computing momentum derivatives of spinor variables.