New Worldsheet Formulae for Conformal Supergravity Amplitudes

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.

arXiv commentv3. minor changes, published in JHEP

References in corpus (34)

• Non-Gaussian features of primordial fluctuations in single field inflationary models
• Perturbative Gauge Theory As A String Theory In Twistor Space
• Scattering of Massless Particles in Arbitrary Dimension
• The Amplituhedron
• On graviton non-Gaussianities during inflation
• Ambitwistor strings and the scattering equations
• On the Tree-Level S-Matrix of Yang-Mills Theory
• An Alternative String Theory in Twistor Space for N=4 Super-Yang-Mills
• Conformal Supergravity in Twistor-String Theory
• Einstein Gravity from Conformal Gravity
• Ambitwistor strings and the scattering equations at one loop
• Loop Integrands for Scattering Amplitudes from the Riemann Sphere
• Ambitwistor strings in 4-dimensions
• Scattering in Three Dimensions from Rational Maps
• Gravity from Rational Curves
• From conformal to Einstein Gravity
• Four Point Functions of the Stress Tensor and Conserved Currents in AdS_4/CFT_3
• A simple formula for gravitational MHV amplitudes
• Conformal and Einstein gravity from twistor actions
• Twistor Strings for N=8 Supergravity
• Gravity On-shell Diagrams
• From Twistor String Theory To Recursion Relations
• Ambitwistor formulations of $R^2$ gravity and $(DF{)}^2$ gauge theories
• On-Shell Diagrams for N = 8 Supergravity Amplitudes
• Conformal Gravity from Gauge Theory
• Einstein supergravity amplitudes from twistor-string theory
• Conformal Supergravity Tree Amplitudes from Open Twistor String Theory
• From 4d Ambitwistor Strings to On Shell Diagrams and Back
• Gravity with a cosmological constant from rational curves
• Twistor/ambitwistor strings and null-superstrings in spacetime of D=4,10 and 11 dimensions
• Twistor-strings and gravity tree amplitudes
• Hidden Conformal Symmetry in Tree-Level Graviton Scattering
• Comments on MHV Tree Amplitudes for Conformal Supergravitons from Topological B-Model
• New Twistor String Theories revisited

Cited by in corpus (5)

• Double copy structure of CFT correlators
• Unraveling conformal gravity amplitudes
• A Monte Carlo Approach to the 4D Scattering Equations
• $\mathcal{N}=7$ On-Shell Diagrams and Supergravity Amplitudes in Momentum Twistor Space
• Analytical amplitudes from numerical solutions of the scattering equations