Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The Off-shell Symmetry Algebra of the Light-cone AdS_5 x S^5 Superstring

Gleb Arutyunov, Sergey Frolov, Jan Plefka, Marija Zamaklar

TL;DR

This work analyzes the off-shell symmetry structure of the AdS5×S5 superstring in the generalized uniform light-cone gauge by relaxing level-matching and taking the infinite-light-cone-momentum limit. Using a hybrid expansion, the authors show that the two copies of the su(2|2) algebra extend centrally by a charge proportional to the level-matching operator, with the Hamiltonian remaining central; this matches the centrally extended algebra expected for the dynamic S-matrix in N=4 gauge theory. The central charge is explicitly derived as c = (1/(2ζ))(e^{ip_ws}−1) (or a boundary-dependent form), and the results recover the Beisert-type algebra in both classical and quantum settings, including the plane-wave limit where no anomalies arise. The analysis clarifies how off-shell string symmetries map to gauge-theory spin-chain structures and highlights the role of the length-changing operator e^{iαx_-} in this correspondence.

Abstract

We analyze the psu(2,2|4) supersymmetry algebra of a superstring propagating in the AdS_5 x S^5 background in the uniform light-cone gauge. We consider the off-shell theory by relaxing the level-matching condition and take the limit of infinite light-cone momentum, which decompactifies the string world-sheet. We focus on the psu(2|2)+psu(2|2) subalgebra which leaves the light-cone Hamiltonian invariant and show that it undergoes extension by a central element which is expressed in terms of the level-matching operator. This result is in agreement with the conjectured symmetry algebra of the dynamic S-matrix in the dual N=4 gauge theory.

The Off-shell Symmetry Algebra of the Light-cone AdS_5 x S^5 Superstring

TL;DR

This work analyzes the off-shell symmetry structure of the AdS5×S5 superstring in the generalized uniform light-cone gauge by relaxing level-matching and taking the infinite-light-cone-momentum limit. Using a hybrid expansion, the authors show that the two copies of the su(2|2) algebra extend centrally by a charge proportional to the level-matching operator, with the Hamiltonian remaining central; this matches the centrally extended algebra expected for the dynamic S-matrix in N=4 gauge theory. The central charge is explicitly derived as c = (1/(2ζ))(e^{ip_ws}−1) (or a boundary-dependent form), and the results recover the Beisert-type algebra in both classical and quantum settings, including the plane-wave limit where no anomalies arise. The analysis clarifies how off-shell string symmetries map to gauge-theory spin-chain structures and highlights the role of the length-changing operator e^{iαx_-} in this correspondence.

Abstract

We analyze the psu(2,2|4) supersymmetry algebra of a superstring propagating in the AdS_5 x S^5 background in the uniform light-cone gauge. We consider the off-shell theory by relaxing the level-matching condition and take the limit of infinite light-cone momentum, which decompactifies the string world-sheet. We focus on the psu(2|2)+psu(2|2) subalgebra which leaves the light-cone Hamiltonian invariant and show that it undergoes extension by a central element which is expressed in terms of the level-matching operator. This result is in agreement with the conjectured symmetry algebra of the dynamic S-matrix in the dual N=4 gauge theory.

Paper Structure

This paper contains 16 sections, 104 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Gauged-fixed string sigma-model
  3. Symmetry generators in the light-cone gauge
  4. General structure of the symmetry generators
  5. Moment map and the Poisson brackets
  6. Explicit basis
  7. Deriving the central charges
  8. Concluding remarks
  9. Appendix
  10. The gauge-fixed Hamiltonian
  11. Symmetry generators
  12. Covariant notation
  13. The explicit form of the $\mathfrak{su}(2|2)_R$ generators
  14. The $\mathfrak{su}(2|2)_R$ supercharge at quartic field order
  15. The explicit form of the $\mathfrak{su}(2|2)_L$ generators
  16. ...and 1 more sections

Figures (1)

  • Figure 1: The distribution of the kinematical and dynamical charges in the ${\cal M}$ supermatrix. The red (dark) and blue (light) blocks correspond to the subalgebra ${\cal J}$ of $\mathfrak{psu}(2,2|4)$ which leaves the Hamiltonian invariant.