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Superparticle and superstring in AdS_3 x S^3 Ramond-Ramond background in light-cone gauge

R. R. Metsaev, A. A. Tseytlin

Abstract

We discuss superparticle and superstring dynamics in AdS_3 x S^3 supported by R-R 3-form background using light-cone gauge approach. Starting with the superalgebra psu(1,1|2) + psu(1,1|2) representing the basic symmetry of this background we find the light-cone superparticle Hamiltonian. We determine the harmonic decomposition of light-cone superfield describing fluctuations of type IIB supergravity fields expanded near AdS_3 x S^3 background and compute the corresponding Kaluza-Klein spectrum. We fix the fermionic and bosonic light-cone gauges in the covariant Green-Schwarz AdS_3 x S^3 superstring action and find the light-cone string Hamiltonian. We also obtain a realization of the generators of psu(1,1|2) + psu(1,1|2) in terms of the superstring 2-d fields in the light-cone gauge.

Superparticle and superstring in AdS_3 x S^3 Ramond-Ramond background in light-cone gauge

Abstract

We discuss superparticle and superstring dynamics in AdS_3 x S^3 supported by R-R 3-form background using light-cone gauge approach. Starting with the superalgebra psu(1,1|2) + psu(1,1|2) representing the basic symmetry of this background we find the light-cone superparticle Hamiltonian. We determine the harmonic decomposition of light-cone superfield describing fluctuations of type IIB supergravity fields expanded near AdS_3 x S^3 background and compute the corresponding Kaluza-Klein spectrum. We fix the fermionic and bosonic light-cone gauges in the covariant Green-Schwarz AdS_3 x S^3 superstring action and find the light-cone string Hamiltonian. We also obtain a realization of the generators of psu(1,1|2) + psu(1,1|2) in terms of the superstring 2-d fields in the light-cone gauge.

Paper Structure

This paper contains 16 sections, 206 equations.

Table of Contents

  1. Introduction
  2. $psu(1,1|2)\oplus\widetilde{psu}(1,1|2)$ superalgebra
  3. Superparticle dynamics in $AdS_3\times S^3$ backrgound
  4. Light-cone gauge superfield formulation of type IIB supergravity on $AdS_3\times S^3$
  5. Quadratic light-cone superfield action
  6. Harmonic decomposition of the light-cone superfield and the spectrum
  7. Light cone superstring action in $AdS_3\times S^3$ R-R background
  8. Fermionic light-cone gauge action in WZ pa-ra-metri-zation
  9. "2-d spinor" form of the action
  10. Fermionic light-cone gauge action in Killing pa-ra-metri-zation
  11. Light cone Hamiltonian approach to superstring in $AdS_3\times S^3$
  12. Phase space Lagrangian
  13. Equations of motion
  14. Noether charges as generators of the superalgebra $psu(1,1|2)\oplus\widetilde{psu}(1,1|2)$
  15. Currents for $\kappa$-symmetry light-cone gauge fixed superstring action
  16. ...and 1 more sections