Solution Transformations for GS String in AdS_5 x S^5 by Conserved Quantities

TL;DR

This paper develops a Hamiltonian framework for a simplified superstring model in AdS_5 x S^5, revealing how conserved quantities generate solution transformations through Poisson brackets.

Contribution

It introduces a Hamiltonian formulation for the light-cone gauge superstring in AdS_5 x S^5, linking conserved quantities to solution transformations via Poisson brackets.

Findings

Derived a linear-velocity Lagrangian after partial Legendre transformation.

Established a Poisson bracket structure for the free, constraint-free system.

Connected infinite conserved quantities to solution transformations using Jacobi identity.

Abstract

For Light-cone gauge of Green-Schwarz superstring in AdS_5 x S^5 background, we fix two bosonic variables x^{+}=\tau and y^{9}=\sigma, and then perform the partial Legendre transformation of the remaining bosonic variables. We then obtain a Lagrangian which is linear in velocity after eliminating the metric of world sheet. For such a system, one can formulate its poisson bracket and Hamiltonian. Since this system is free and without constraint, the hierarchy of infinite nonlocal conserved quantities given by Bena, Polchinski and Roiban, induce solution transformations due to Jacobi identity.