Foundations of the AdS_5 x S^5 Superstring. Part I

TL;DR

This article lays the classical foundation for the AdS5 x S5 superstring, formulating it as a PSU(2,2|4)/SO(4,1)xSO(5) coset and establishing its integrable structure through a Z4 grading, Lax pair, and κ-symmetry. It develops the light-cone gauge quantization, derives the exact worldsheet S-matrix up to a scalar dressing factor, and analyzes the spectrum in both plane and finite-size (cylinder) settings, including giant magnons and multicomponent closed sectors. The work connects the string side to the dual N=4 SYM via centrally extended su(2|2) algebras and prepares a robust framework for non-perturbative spectral approaches like TBA and Y-systems in Part II. Overall, it provides a self-contained, technically detailed toolkit for computing the AdS5 x S5 string spectrum and its gauge-theory correspondence.

Abstract

We review the recent advances towards finding the spectrum of the AdS_5 x S^5 superstring. We thoroughly explain the theoretical techniques which should be useful for the ultimate solution of the spectral problem. In certain cases our exposition is original and cannot be found in the existing literature. The present Part I deals with foundations of classical string theory in AdS_5 x S^5, light-cone perturbative quantization and derivation of the exact light-cone world-sheet scattering matrix.

Figures (8)

• Figure 1: The AdS/CFT correspondence: The spectrum of a 2d non-linear sigma-model describing string theory on a curved background is expected to be equivalent to the spectrum of a 4d quantum non-abelian gauge theory in the large $N$ limit.
• Figure 2: Solitonic excitations of a closed string in the decompactification limit.
• Figure 3: 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.
• Figure 4: Factorization of the multi-particle scattering.
• Figure 5: In the collision process particles either keep (transition) or exchange (reflection) their momenta. The S-matrix operates non-trivially in the flavor space.