Twistor action for general relativity
arXiv:2104.07031
Abstract
We reformulate Euclidean general relativity without cosmological constant as an action governing the complex structure of twistor space. Extending Penrose's non-linear graviton construction, we find a correspondence between twistor spaces with partially integrable almost complex structures and four-dimensional space-times with off-shell metrics. Using this, we prove that our twistor action reduces to Plebanski's action for general relativity via the Penrose transform. This should lead to new insights into the geometry of graviton scattering as well as to the derivation of computational tools like gravitational MHV rules.
arXiv comment6 pages, no figures; v2: corrections
References in corpus (24)
- MHV Vertices And Tree Amplitudes In Gauge Theory
- On the Tree-Level S-Matrix of Yang-Mills Theory
- The Complete Planar S-matrix of N=4 SYM as a Wilson Loop in Twistor Space
- An Alternative String Theory in Twistor Space for N=4 Super-Yang-Mills
- Ambitwistor strings in 4-dimensions
- From Twistor Actions to MHV Diagrams
- Gravity from Rational Curves
- A Twistorial Foundation for the Classical Double Copy
- A Proof of the Supersymmetric Correlation Function / Wilson Loop Correspondence
- Gravity in Twistor Space and its Grassmannian Formulation
- Twistor Actions for Self-Dual Supergravities
- Conformal and Einstein gravity from twistor actions
- Twistor Strings for N=8 Supergravity
- The twistorial structure of loop-gravity transition amplitudes
- MHV diagrams in twistor space and the twistor action
- Composite Operators in the Twistor Formulation of SYM Theory
- MHV scattering of gluons and gravitons in chiral strong fields
- Twistor methods for AdS
- Self-Dual Supergravity and Twistor Theory
- Gravity with a cosmological constant from rational curves
- A Twistorial Approach to Integrability in N=4 SYM
- Twistor actions for gauge theory and gravity
- Minitwistors and 3d Yang-Mills-Higgs theory
- Chiral perturbation theory for GR