2T Physics Formulation of Superconformal Dynamics Relating to Twistors and Supertwistors

TL;DR

This paper presents a 2T physics framework that reformulates superconformal dynamics using supertwistor variables, unifying different descriptions and enabling quantization via oscillator formalism for supergroups.

Contribution

It introduces a 2T physics approach to express superconformal dynamics in terms of supertwistors, connecting gauge transformations and quantization methods.

Findings

Superconformal symmetries are realized as gauge symmetries in 2T physics.

Supertwistor variables can be gauge transformed into superspace coordinates and momenta.

Quantization corresponds to oscillator formalism for non-compact supergroups.

Abstract

The conformal symmetry SO(d,2) of the massless particle in d dimensions, or superconformal symmetry OSp(N|4), SU(2,2|N), OSp(8|N) of the superparticle in d=3,4,6 dimensions respectively, had been previously understood as the global Lorentz symmetry and supersymmetries of 2T physics in d+2 dimensions. By utilising the gauge symmetries of 2T physics, it is shown that the dynamics can be cast in terms of superspace coordinates, momenta and theta variables or in terms of supertwistor variables a la Penrose and Ferber. In 2T physics these can be gauge transformed to each other. In the supertwistor version the quantization of the model amounts to the well known oscillator formalism for non-compact supergroups.