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Sine-Gordon-like action for the Superstring in AdS(5) x S(5)

Andrei Mikhailov, Sakura Schafer-Nameki

TL;DR

This work presents a relativistically invariant, sine-Gordon–like action for the Green-Schwarz-Metsaev-Tseytlin string on AdS5×S5, realized as a mass-deformed gauged WZW model for SO(4,1)×SO(5)/SO(4)×SO(4) with fermions. It shows that the classical GSMT equations of motion are reproduced by the proposed action and interprets the model through the boost-invariant Poisson structure and Hamiltonian reduction of WZW theory. The authors relate their construction to the Bakas–Park–Shin framework, discuss the infinite-worldsheet formalism, and extend the formulation to fermions, including explicit equations of motion and current constraints. They also clarify the classical–quantum caveats, such as differences in Poisson structures and the need for further work to establish world-sheet supersymmetry and quantum integrability. The approach provides a new, relativistic, integrable perspective on GSMT string dynamics with potential implications for conserved charges and future quantization.

Abstract

We propose an action for a sine-Gordon-like theory, which reproduces the classical equations of motion of the Green-Schwarz-Metsaev-Tseytlin superstring on AdS(5) x S(5). The action is relativistically invariant. It is a mass-deformed gauged WZW model for SO(4,1) x SO(5) / SO(4) x SO(4) interacting with fermions.

Sine-Gordon-like action for the Superstring in AdS(5) x S(5)

TL;DR

This work presents a relativistically invariant, sine-Gordon–like action for the Green-Schwarz-Metsaev-Tseytlin string on AdS5×S5, realized as a mass-deformed gauged WZW model for SO(4,1)×SO(5)/SO(4)×SO(4) with fermions. It shows that the classical GSMT equations of motion are reproduced by the proposed action and interprets the model through the boost-invariant Poisson structure and Hamiltonian reduction of WZW theory. The authors relate their construction to the Bakas–Park–Shin framework, discuss the infinite-worldsheet formalism, and extend the formulation to fermions, including explicit equations of motion and current constraints. They also clarify the classical–quantum caveats, such as differences in Poisson structures and the need for further work to establish world-sheet supersymmetry and quantum integrability. The approach provides a new, relativistic, integrable perspective on GSMT string dynamics with potential implications for conserved charges and future quantization.

Abstract

We propose an action for a sine-Gordon-like theory, which reproduces the classical equations of motion of the Green-Schwarz-Metsaev-Tseytlin superstring on AdS(5) x S(5). The action is relativistically invariant. It is a mass-deformed gauged WZW model for SO(4,1) x SO(5) / SO(4) x SO(4) interacting with fermions.

Paper Structure

This paper contains 20 sections, 73 equations, 1 figure.

Table of Contents

  1. Introduction and Summary
  2. The boost-invariant symplectic structure of the Metsaev-Tseytlin superstring
  3. Classical superstring in terms of currents
  4. Geometrical meaning of $J_{\pm}$ and $\nabla_{\pm}$
  5. Poisson brackets in the lightcone description
  6. The action giving rise to the boost-invariant Poisson bracket
  7. The action of Bakas, Park and Shin
  8. An equivalent form of the string worldsheet equations of motion.
  9. Gauged WZW with a mass term
  10. Relation between string worldsheet theory and gauged WZW: formal analysis on an infinite worldsheet
  11. Interpretation as Hamiltonian reduction of WZW model
  12. Including fermions
  13. Fermionic terms in the action
  14. Equations of motion
  15. Variation with respect to $A_{\pm}$
  16. ...and 5 more sections

Figures (1)

  • Figure 1: The classical string phase space is shown as a horizontal plane; each point on the plane corresponds to the phase space of the Hamiltonian reduction of WZW for the value of the moment map $([m_L],[m_R])$. The phase space of the gauged WZW is mapped on the subspace $[m_L]=[m_R]$ of codimension $rk(\mathfrak{h})$. The map involves identification of the points related by the action of $U(1)^{rk(\mathfrak{h})}$.