Spin chains and string theory

TL;DR

This paper demonstrates a precise correspondence between rotating strings in AdS5xS5 and spin chain models in N=4 SYM, using sigma models and semi-classical states to deepen the understanding of AdS/CFT duality.

Contribution

It introduces a sigma model approach to solve the Heisenberg spin chain and connects it to string theory, providing a more complete picture of the AdS/CFT correspondence.

Findings

Heisenberg chain solved by sigma model matches string rotating with large angular momentum.

Large angular momentum limit yields the same sigma model as the string.

Mean spin value corresponds to the string's position in the bulk.

Abstract

Recently, an impressive agreement was found between anomalous dimensions of certain operators in N=4 SYM and rotating strings with two angular momenta in the bulk of AdS5xS5. A one-loop field theory computation, which involves solving a Heisenberg chain by means of the Bethe ansatz agrees with the large angular momentum limit of a rotating string. We point out that the Heisenberg chain can be equally well solved by using a sigma model approach. Moreover we also show that a certain limit, akin to the BMN limit, leads exactly to the same sigma model for a string rotating with large angular momentum. The agreement is then at the level of the action. As an upshot we propose that the rotating string should be identified with a coherent, semi-classical state built out of the eigenstates of the spin chain. The agreement is then complete. For example we show that the mean value of the spin <S> gives, precisely, the position of the string in the bulk. This suggests a more precise formulation of the AdS/CFT correspondence in the large-N limit and also indicates a way to obtain string theory duals of other gauge theories.