On the Spectrum of the AdS_5xS^5 String at large lambda

TL;DR

This paper develops a perturbative quantization approach for the bosonic sector of the IIB superstring on AdS_5xS^5 in the large radius limit, analyzing the spectrum and conformal dimensions with a focus on the Konishi state.

Contribution

It introduces a method for quantizing the string in the large radius limit and computes the spectrum and conformal dimensions, including leading and sub-leading corrections.

Findings

Derived the bosonic string Hamiltonian in the large R limit.

Calculated the conformal dimension of the Konishi state at leading and sub-leading orders.

Identified ordering ambiguities preventing determination of certain spectrum corrections.

Abstract

We put forth a program for perturbatively quantizing the bosonic sector of the IIB superstring on AdS_5xS^5 in the large radius of curvature R (i.e. flat-space) limit, and in light-cone gauge. Using the quantization of the massive particle on AdS_5xS^5 as a guiding exercise, we read off the correct scaling of the particle coordinates in the large radius limit. In the corresponding large \sqrt{\lambda}=R^2/\alpha' limit of the string the oscillator modes must be scaled differently from the zero modes. We compute the bosonic string Hamiltonian in this limit which gives the flat-space mass-squared operator at leading order, followed by a harmonic oscillator potential in the zero modes at subleading order. Using these ingredients we calculate the leading and sub-leading terms in the conformal dimension of the length-four Konishi state in the large-\lambda limit. Furthermore we work out the relevant terms of the energy expansion to next-to-next-to leading order, which are plagued by severe ordering ambiguities. This prevents us from determining the corrections to the spectrum at order {\lambda}^{-1/4}.