New worldsheet formulae for conformal supergravity amplitudes. (English) Zbl 1395.83123
Summary: 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.
MSC:
| 83E50 | Supergravity |
| 53Z05 | Applications of differential geometry to physics |
| 83E30 | String and superstring theories in gravitational theory |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81R25 | Spinor and twistor methods applied to problems in quantum theory |
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