Classical Exchange Algebra of the Superstring on S^5 with the AdS-time

TL;DR

This paper derives a classical exchange algebra for the superstring on S^5 with AdS-time using a geometrical approach, ensuring consistency via the classical Yang-Baxter equation, and discusses the limitations of the Dirac method.

Contribution

It introduces a geometrical method to establish the classical exchange algebra for the superstring on S^5 with AdS-time, overcoming Dirac method constraints.

Findings

Classical exchange algebra derived on the light-like plane.

Geometrical method guarantees consistency via the classical Yang-Baxter equation.

Dirac method is ineffective due to complex constraints.

Abstract

A classical exchange algebra of the superstring on S^5 with the AdS-time is shown on the light-like plane. To this end we use the geometrical method of which consistency is guaranteed by the classical Yang-Baxter equation. The Dirac method does not work, there being constraints which contain first-class and second-class and one can disentangle with each other keeping the isometry hardly.