Hamiltonian dynamics and the hidden symmetries of the AdS_5 x S^5 superstring

TL;DR

This paper constructs a Hamiltonian formalism-based Lax connection for the AdS_5 x S^5 superstring, revealing hidden symmetries and ensuring integrability through first-class conserved quantities.

Contribution

It introduces a modified Lax connection that differs from previous versions by Hamiltonian constraint terms, ensuring flatness and first-class integrals of motion.

Findings

Lax connection constructed within Hamiltonian formalism

Ensures all integrals of motion are first class

Lax connection is flat in the strong sense

Abstract

We construct the Lax connection of the Green-Schwarz superstring in AdS_5 x S^5 within the Hamiltonian formalism and obtain precisely that used in 0810.4136. It differs in a crucial way from the Bena-Polchinski-Roiban connection by terms proportional to the Hamiltonian constraints. These extra terms ensure firstly that the integrals of motion are all first class and secondly that the Lax connection is flat in the strong sense.