New worldsheet formulae for conformal supergravity amplitudes
- 39 Downloads
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.
KeywordsScattering Amplitudes Conformal Field Models in String Theory Supergravity Models
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.
- S.J. Parke and T.R. Taylor, An Amplitude for n Gluon Scattering, Phys. Rev. Lett. 56 (1986) 2459 [INSPIRE].
- D.B. Fairlie and D.E. Roberts, Dual Models Without Tachyons — A New Approach, PRINT-72-2440 [INSPIRE].
- D.J. Gross and P.F. Mende, The High-Energy Behavior of String Scattering Amplitudes, Phys. Lett. B 197 (1987) 129 [INSPIRE].
- E. Bergshoeff, M. de Roo and B. de Wit, Extended Conformal Supergravity, Nucl. Phys. B 182 (1981) 173 [INSPIRE].
- E.S. Fradkin and A.A. Tseytlin, Conformal Anomaly in Weyl Theory and Anomaly Free Superconformal Theories, Phys. Lett. B 134 (1984) 187 [INSPIRE].
- M.T. Anderson L 2 curvature and volume renormalization of AHE metrics on 4-manifolds, Math. Res. Lett. 8 (2001) 171 [math/0011051].