Current Algebra of the Pure Spinor Superstring in AdS(5) x S(5)

TL;DR

This paper conducts a Hamiltonian analysis of the classical pure spinor superstring in AdS(5) x S(5), elucidating its symmetries, constraints, and algebraic structures within a canonical framework.

Contribution

It provides a detailed Hamiltonian formulation, including Poisson brackets and constraints, of the pure spinor superstring in AdS(5) x S(5), highlighting symmetry generators and their algebra.

Findings

Identified first class constraints related to local symmetry groups.

Derived classical graded Poisson brackets of currents and ghosts.

Discussed the structure of global PSU(2,2|4) symmetry and Yangian extension.

Abstract

We perform a Hamiltonian analysis of the classical type IIB superstring on AdS(5) x S(5) in the pure spinor approach. Taking the spatial components of the left-invariant (super)currents and the pure spinor ghosts as canonical variables, we compute the classical graded Poisson brackets of the currents and ghosts and identify the first class constraints associated to the local SO(4,1) x SO(5) symmetry and the pure spinor condition. We then study the properties of the BRST generators and the Hamiltonian along the constraints. For a natural choice of the the Lagrange multipliers, we show equivalence of the canonical equations of motion with the covariant ones. Finally we briefly discuss the (non) local currents, including the ghost contribution, that generate the global PSU(2,2|4) symmetry and its Yangian extension in the present framework.