Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Bihamiltonian structure of the classical superstring in AdS_5 x S**5

Andrei Mikhailov

TL;DR

The paper establishes a bihamiltonian framework for the classical superstring in AdS_5 x S^5 by deriving a boost-invariant symplectic structure and decomposing the canonical Poisson bracket into three compatible brackets with distinct scaling. It shows how the boost-invariant bracket relates to a chiral WZW (Kirillov) bracket through Hamiltonian reduction and connects the monodromy matrix to integrability via Casimir functionals. A detailed analysis of the AdS_5 x S^5 current algebra psu(2,2|4) and its Z_4 grading underpins the construction, including gauge and dressing transformations and the handling of fermionic degrees of freedom. The work culminates in a geometric interpretation of the boost-invariant Poisson bracket for the bosonic sector, tying the algebraic bihamiltonian structure to the underlying differential-geometric data of the string worldsheet and its normal frames.

Abstract

We discuss the bihamiltonian structure of the Metsaev-Tseytlin superstring in AdS_5 x S**5. We explicitly write down the boost-invariant symplectic structure for the superstring in AdS_5 x S**5 and explain its relation to the standard (canonical) symplectic structure. We discuss the geometrical meaning of the boost-invariant symplectic structure for the bosonic string.

Bihamiltonian structure of the classical superstring in AdS_5 x S**5

TL;DR

The paper establishes a bihamiltonian framework for the classical superstring in AdS_5 x S^5 by deriving a boost-invariant symplectic structure and decomposing the canonical Poisson bracket into three compatible brackets with distinct scaling. It shows how the boost-invariant bracket relates to a chiral WZW (Kirillov) bracket through Hamiltonian reduction and connects the monodromy matrix to integrability via Casimir functionals. A detailed analysis of the AdS_5 x S^5 current algebra psu(2,2|4) and its Z_4 grading underpins the construction, including gauge and dressing transformations and the handling of fermionic degrees of freedom. The work culminates in a geometric interpretation of the boost-invariant Poisson bracket for the bosonic sector, tying the algebraic bihamiltonian structure to the underlying differential-geometric data of the string worldsheet and its normal frames.

Abstract

We discuss the bihamiltonian structure of the Metsaev-Tseytlin superstring in AdS_5 x S**5. We explicitly write down the boost-invariant symplectic structure for the superstring in AdS_5 x S**5 and explain its relation to the standard (canonical) symplectic structure. We discuss the geometrical meaning of the boost-invariant symplectic structure for the bosonic string.

Paper Structure

This paper contains 25 sections, 135 equations.

Table of Contents

  1. Introduction
  2. General facts about Poisson brackets and symplectic structure
  3. Symplectic form
  4. Poisson bracket
  5. The lightcone approach to the description of the symplectic structure
  6. Compatibility of Poisson brackets
  7. Classical string on ${\bf R}\times S^N$, the nonlinear $\sigma$-model and the generalized sine-Gordon system
  8. Classical string and nonlinear $\sigma$-model
  9. Classical string and generalized sine-Gordon
  10. Relativistic symmetry
  11. Superstring in $AdS_5\times S^5$
  12. The superalgebra ${\bf g}=psu(2,2|4)$
  13. Classical action and the canonical symplectic structure
  14. Gauge transformations and dressing transformations
  15. Bihamiltonian structure of the classical superstring
  16. ...and 10 more sections