Light-cone Superstring in AdS Space-time

TL;DR

This paper develops a phase-space, light-cone gauge formulation for strings in AdS_5 x S^5 and AdS_3 x S^3, fixing x^+ = τ and distributing P^+ uniformly to construct a well-defined Hamiltonian framework. It first treats the bosonic string in curved backgrounds and then extends to the IIB superstring by adopting a κ-symmetry gauge that yields a tractable phase-space action, derives the phase-space Lagrangian, equations of motion, and explicit light-cone Hamiltonians (including AdS_3 x S^3 RR backgrounds). It also provides a detailed Noether analysis, constructing the psu(2,2|4) symmetry charges via currents and their integrated charges, clarifying how dynamical generators arise from kinematic ones through the algebra. The results offer concrete tools for exploring the AdS/CFT correspondence at the string level, including the particle limit, potential links to integrable structures, and a basis for string-field formulations in symmetric AdS backgrounds.

Abstract

We consider fixing the bosonic light-cone gauge for string in AdS in the phase space framework, i.e. by choosing $x^+ = τ$, and by choosing $σ$ so that $P^+$ is distributed uniformly (its density is independent of $σ$). We discuss classical bosonic string in AdS space and superstring in AdS_5 x S^5. In the latter case the starting point is the action found in hep-th/0007036 where the kappa-symmetry is fixed by a fermionic light cone gauge. We derive the light cone Hamiltonian in the AdS_5 x S^5 case and in the case of superstring in AdS_3 x S^3. We also obtain a realization of the generators of the basic symmetry superalgebra psu(2,2|4) in terms of the AdS_5 x S^5 superstring coordinate fields.