String bits in small radius AdS and weakly coupled N=4 Super Yang-Mills Theory: I

TL;DR

This paper investigates the quantization of IIB strings in AdS_5 imes S^5 at small radius, revealing a string-bit picture, analyzing spectra, and exploring perturbative corrections to test the AdS/CFT correspondence.

Contribution

It introduces a string-bit framework in the small radius limit, constructs spectra, and computes perturbative corrections, advancing the understanding of string and gauge theory duality.

Findings

String bits behave as superparticles with discrete spectra at zero radius.

Perturbative corrections at small radius are finite and cancel boundary divergences.

The framework offers a potential approach to rigorously test the AdS/CFT conjecture.

Abstract

We study light-cone gauge quantization of IIB strings in AdS_5 \times S^5 for small radius in Poincare coordinates. A picture of strings made up of noninteracting bits emerges in the zero radius limit. In this limit, each bit behaves like a superparticle moving in the AdS_5 \times S^5 background, carrying appropriate representations of the super conformal group PSU(2,2|4). The standard Hamiltonian operator which causes evolution in the light-cone time has continuous eigenvalues and provides a basis of states which is not suitable for comparing with the dual super Yang-Mills theory. However, there exist operators in the light-cone gauge which have discrete spectra and can be used to label the states. We obtain the spectrum of single bit states and construct multi-bit states in this basis. There are difficulties in the construction of string states from the multi-bit states, which we discuss. A non-zero value of the radius introduces interactions between the bits and the spectrum of multi-bit states gets modified. We compute the leading perturbative corrections at small radius for a few simple cases. Potential divergences in the perturbative corrections, arising from strings near the boundary, cancel. This encourages us to believe that our perturbative treatment could provide a framework for a rigorous and detailed testing of the AdS/CFT conjecture, once the difficulties in the construction of string states are resolved.