The Classical Exchange Algebra of AdS5 x S5 String Theory

TL;DR

This paper derives the classical exchange algebra for AdS5 x S5 string theory in both Green-Schwarz and pure spinor formulations, demonstrating conserved charges are in involution and comparing different approaches.

Contribution

It provides a unified derivation of the classical exchange algebra for AdS5 x S5 string theory in two formulations, showing conserved charges are in involution.

Findings

Classical exchange algebra determined for Green-Schwarz formulation.

Exchange algebra also derived within pure spinor formulation.

Conserved charges are shown to be in involution.

Abstract

The classical exchange algebra satisfied by the monodromy matrix of AdS5 x S5 string theory in the Green-Schwarz formulation is determined by using a first-order Hamiltonian formulation and by adding to the Bena-Polchinski-Roiban Lax connection terms proportional to constraints. This enables in particular to show that the conserved charges of this theory are in involution. This result is obtained for a general world-sheet metric. The same exchange algebra is obtained within the pure spinor description of AdS5 x S5 string theory. These results are compared to the one obtained by A. Mikhailov and S. Schaefer-Nameki for the pure spinor formulation.