Palatial twistor theory and the twistor googly problem

Area of Science:

• Theoretical Physics
• Mathematical Physics
• String Theory

Background:

• The twistor program aims to describe fundamental physics using twistor geometry.
• A significant challenge, the 'googly problem', has hindered the description of right-handed massless fields (positive helicity) within this framework for nearly 40 years.
• Existing twistor constructions, like the nonlinear graviton and Ward constructions, successfully describe left-handed fields (negative helicity) but not right-handed ones.

Purpose of the Study:

• To propose a novel theoretical framework, palatial twistor theory, to resolve the 'googly problem'.
• To provide a twistor description for right-handed interacting massless fields.
• To extend conventional twistor theory to accommodate positive helicity fields.

Main Methods:

• Introduction of palatial twistor theory, a new approach within the twistor program.
• Incorporation of a non-commutative holomorphic quantized twistor 'Heisenberg algebra'.
• Extension of conventional twistor theory's holomorphic functions to include operators of twistor differentiation.

Main Results:

• An explicit proposal for palatial twistor theory is presented.
• The theory is illustrated with a specific application to gravitation.
• The proposed framework successfully addresses the long-standing 'googly problem'.

Conclusions:

• Palatial twistor theory offers a viable solution to the 'googly problem' in twistor theory.
• This new theory enables a twistor description for right-handed massless fields.
• The incorporation of non-commutative algebraic structures and twistor differentiation operators represents a significant advancement in twistor theory.