Lightcone Quantization of String Theory Duals of Free Field Theories

TL;DR

This work investigates the AdS/CFT dual in the zero-curvature-radius limit by explicitly quantizing the bosonic string on AdS in light-cone gauge. In the limit $\lambda \rightarrow 0$, the worldsheet decouples into an infinite set of free partons, and the string Hilbert space maps to the light-front Fock space of a free matrix scalar, with the extra-dimensional momentum encoding light-cone momentum fractions. The resulting spectrum precisely matches the single-trace sector of the dual free field theory (open strings to fundamental matter, closed strings to adjoints), and the author provides a detailed mapping between string modes and parton degrees of freedom, outlining how interactions could be incorporated via perturbations in $\lambda$ and $g_s$. This work offers a concrete realization of a weakly coupled dual description and sets the stage for incorporating fermions to recover gauge theories like YM, as well as exploring substry AdS backgrounds; it also highlights subtleties related to twisted sectors and conformal anomalies in the light-cone formulation.

Abstract

We quantize in light cone gauge the bosonic sector of string theory on Anti-de Sitter space in the zero curvature radius limit. We find that the worldsheet falls apart into a theory of free partons and map the Hilbert space of the string theory to the Hilbert space of a free scalar in light-front description. We outline how the string worldsheet reproduces the field theory at weak coupling.