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New worldsheet formulae for conformal supergravity amplitudes

Farrow, Joseph A.; Lipstein, Arthur E.

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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.


Farrow, J. A., & Lipstein, A. E. (2018). New worldsheet formulae for conformal supergravity amplitudes. Journal of High Energy Physics, 2018(7), Article 074.

Journal Article Type Article
Acceptance Date Jul 6, 2018
Online Publication Date Jul 11, 2018
Publication Date Jul 11, 2018
Deposit Date Jul 11, 2018
Publicly Available Date Jul 12, 2018
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2018
Issue 7
Article Number 074


Published Journal Article (420 Kb)

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Copyright Statement
© The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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