# Palatial twistor theory and the twistor googly problem

@article{Penrose2015PalatialTT, title={Palatial twistor theory and the twistor googly problem}, author={Roger Penrose}, journal={Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences}, year={2015}, volume={373} }

A key obstruction to the twistor programme has been its so-called ‘googly problem’, unresolved for nearly 40 years, which asks for a twistor description of right-handed interacting massless fields (positive helicity), using the same twistor conventions that give rise to left-handed fields (negative helicity) in the standard ‘nonlinear graviton’ and Ward constructions. An explicit proposal for resolving this obstruction—palatial twistor theory—is put forward (illustrated in the case of…

## 16 Citations

### Twistor Theory as an Approach to Fundamental Physics

- Mathematics
- 2018

The original motivations underlying the introduction of twistor theory are described, demanding a (3+1)-dimensional space-time theory dependent upon complex analysis and geometry. Space-time points…

### Lectures on twistor theory

- Physics
- 2017

Broadly speaking, twistor theory is a framework for encoding physical information on space-time as geometric data on a complex projective space, known as a twistor space. The relationship between…

### Twistor theory at fifty: from contour integrals to twistor strings

- MathematicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2017

The Newtonian limit of twistor theory is discussed and its possible role in Penrose’s proposal for a role of gravity in quantum collapse of a wave function is discussed.

### Twistor action for general relativity

- Physics
- 2021

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…

### Newtonian Twistor Theory

- Mathematics
- 2017

In twistor theory the nonlinear graviton construction realises four-dimensional anti-self-dual
Ricci-flat manifolds as Kodaira moduli spaces of rational curves in three-dimensional complex
manifolds.…

### Celestial w1+∞ Symmetries from Twistor Space

- MathematicsSymmetry, Integrability and Geometry: Methods and Applications
- 2022

. We explain how twistor theory represents the self-dual sector of four dimensional gravity in terms of the loop group of Poisson diﬀeomorphisms of the plane via Penrose’s nonlinear graviton…

### Palatial Twistors from Quantum Inhomogeneous Conformal Symmetries and Twistorial DSR Algebras

- MathematicsSymmetry
- 2021

The recently introduced palatial NC twistors are constructed by considering the pair of conjugated (Born-dual) twist-deformed D=4 quantum inhomogeneous conformal Hopf algebras and the quantum deformations of Heisenberg-conformal algebra (HCA) su(2,2)⋉T4,4 are introduced providing in twistorial framework the basic covariant quantum elementary system.

### Twistor sigma models for quaternionic geometry and graviton scattering

- Mathematics
- 2021

We reformulate the twistor construction for hyperand quaternion-Kähler manifolds, introducing new sigma models that compute scalar potentials for the geometry. These sigma models have the twistor…

### Symplectic Measures of Contact with Noether

- Physics
- 2020

Witten’s covariant symplectic formalism is used to compare a set of cohomologous chiral first-order Lagrangians for gravity through their symplectic structures and thus Liouville/GHS measures that…

### Twistors and amplitudes

- PhysicsPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2015

A brief review is given of why twistor geometry has taken a central place in the theory of scattering amplitudes for fundamental particles and the development of which has now led to the definition by Arkani-Hamed et al. of the ‘amplituhedron’.

## References

SHOWING 1-10 OF 13 REFERENCES

### Twistor quantisation and curved space-time

- Physics
- 1968

AbstractThe formalism of twistors [the ‘spinors’ for the group O(2,4)] is employed to give a concise expression for the solution of the zero rest-mass field equations, for each spin (s=0, 1/2, 1,…

### Noncommutative geometry and reality

- Mathematics
- 1995

We introduce the notion of real structure in our spectral geometry. This notion is motivated by Atiyah’s KR‐theory and by Tomita’s involution J. It allows us to remove two unpleasant features of the…

### Self-dual gauge fields

- Physics
- 1980

Using ideas and techniques adopted from the theory of self-dual gravitational fields we investigate properties of self-dual gauge fields. A linear equation which generates these fields is the center…

### Book-Review - Spinors and Spacetime - VOL.2 - Spinor and Twistor Methods in Spacetime Geometry

- Physics
- 1986

### Two-spinor calculus and relativistic fields

- Physics
- 1984

Preface 1. The geometry of world-vectors and spin-vectors 2. Abstract indices and spinor algebra 3. Spinors and world-tensors 4. Differentiation and curvature 5. Fields in space-time Appendix…

### Spinor and twistor methods in space-time geometry

- Mathematics
- 1986

Preface Summary of volume 1 6. Twistors 7. Null congruences 8. Classification of curvature tensors 9. Conformal infinity Appendix References Subject and author index Index of symbols.

### The domain of dependence

- Mathematics
- 1970

The various properties of the domain of dependence (Cauchy development) which have been found particularly useful in the study of gravitational fields are reviewed. The basic techniques for…

### Self-dual space-times with cosmological constant

- Physics, Mathematics
- 1980

It is shown that self-dual solutions of Einstein's equations, with cosmological constant λ, correspond to certain complex manifolds. This result generalizes the work of Penrose [1], who dealt with…

### Geometric quantization, 2nd edn

- 1991