Two-twistor description of a membrane

This paper forms a part of the twistor programme whereby constructions of physics on Minkowski space are transferred, it is hoped, to simpler constructions on Penrose’s twistor-space . We show how the Penrose transform may be used to describe solutions of the Dirac equations on Minkowski space in terms of certain cohomology classes on a related five-dimensional complex manifold. This is accomplished along the same lines as the corresponding representation of massless fields. It means that Penrose’s integral formulae for massive fields may be interpreted cohomologically. We also give a brief discussion of the spin operator in twistor space.

Download Full-text

Palatial twistor theory and the twistor googly problem

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2014.0237 ◽

2015 ◽

Vol 373 (2047) ◽

pp. 20140237 ◽

Cited By ~ 5

Author(s):

Roger Penrose

Keyword(s):

Holomorphic Functions ◽

Heisenberg Algebra ◽

Twistor Theory ◽

Negative Helicity ◽

Nonlinear Graviton ◽

Twistor Description ◽

Massless Fields

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 gravitation). This incorporates the concept of a non-commutative holomorphic quantized twistor ‘Heisenberg algebra’, extending the sheaves of holomorphic functions of conventional twistor theory to include the operators of twistor differentiation.

Download Full-text

A pure spinor twistor description of the D = 10 superparticle

Journal of High Energy Physics ◽

10.1007/jhep08(2020)130 ◽

2020 ◽

Vol 2020 (8) ◽

Author(s):

Diego García Sepúlveda ◽

Max Guillen

Keyword(s):

Pure Spinor ◽

Yang Mills ◽

Twistor Description ◽

Field Redefinition

Abstract We present a novel twistor formulation of the ten-dimensional massless super-particle. This formulation is based on the introduction of pure spinor variables through a field redefinition of another model for the superparticle, and in the new description we find that the super-Pauli-Lubanski three-form naturally arises as a constraint. Quantization is studied in detail for both models and they are shown to correctly describe the D = 10 super-Yang-Mills states.

Download Full-text