# New worldsheet formulae for conformal supergravity amplitudes

Journal of High Energy Physics, Jul 2018

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.

This is a preview of a remote PDF: https://link.springer.com/content/pdf/10.1007%2FJHEP07%282018%29074.pdf

Joseph A. Farrow, Arthur E. Lipstein. New worldsheet formulae for conformal supergravity amplitudes, Journal of High Energy Physics, 2018, 74, DOI: 10.1007/JHEP07(2018)074