Spin chains and string theory

Details Spin chains and string theory Spin chains and string theory

2003-11-23

arxiv.org/abs/hep-th/0311203v3

Phys.Rev.Lett. 93 (2004) 161602

Physics

High Energy Physics

High Energy Physics - Theory

16 pages. LaTeX. v2: References and some comments added. v3: References to more recent work added

Scientific paper

10.1103/PhysRevLett.93.161602

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 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.