Twistorial versus space--time formulations: unification of various string models

TL;DR

This paper introduces a twistorial formulation of the D=4 bosonic string, demonstrating its equivalence to existing models and deriving related formulations through gauge fixing, thereby unifying various string descriptions.

Contribution

It presents a novel twistorial tensionful bosonic string model and establishes its equivalence to known string models, unifying different formulations within a twistorial framework.

Findings

Equivalent to Siegel's covariant string model

Derives SSTV and BZ string models from the twistorial formulation

Provides a unified twistorial approach to various string models

Abstract

We introduce the D=4 twistorial tensionfull bosonic string by considering the canonical twistorial 2--form in two--twistor space. We demonstrate its equivalence to two bosonic string models: due to Siegel (with covariant worldsheet vectorial string momenta $P_\mu^{m}(\tau,\sigma)$) and the one with tensorial string momenta $P_{[\mu\nu]}(\tau,\sigma)$. We show how to obtain in mixed space-time--twistor formulation the Soroka--Sorokin--Tkach--Volkov (SSTV) string model and subsequently by harmonic gauge fixing the Bandos--Zheltukhin (BZ) model, with constrained spinorial coordinates.