New worldsheet formulae for conformal supergravity amplitudes

  • Joseph A. Farrow
  • Arthur E. LipsteinEmail author
Open Access
Regular Article - Theoretical Physics


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.


Scattering Amplitudes Conformal Field Models in String Theory Supergravity Models 


Open Access

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Department of Mathematical SciencesDurham UniversityDurhamUnited Kingdom

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