Quantum folded string and integrability: from finite size effects to Konishi dimension
Abstract
Using the algebraic curve approach we one-loop quantize the folded string solution for the type IIB superstring in AdS(5)xS(5). We obtain an explicit result valid for arbitrary values of its Lorentz spin S and R-charge J in terms of integrals of elliptic functions. Then we consider the limit S ~ J ~ 1 and derive the leading three coefficients of strong coupling expansion of short operators. Notably, our result evaluated for the anomalous dimension of the Konishi state gives 2\lambda^{1/4}-4+2/\lambda^{1/4}. This reproduces correctly the values predicted numerically in arXiv:0906.4240. Furthermore we compare our result using some new numerical data from the Y-system for another similar state. We also revisited some of the large S computations using our methods. In particular, we derive finite--size corrections to the anomalous dimension of operators with small J in this limit.
Cite
@article{arxiv.1102.1040,
title = {Quantum folded string and integrability: from finite size effects to Konishi dimension},
author = {Nikolay Gromov and Didina Serban and Igor Shenderovich and Dmytro Volin},
journal= {arXiv preprint arXiv:1102.1040},
year = {2011}
}
Comments
20 pages, 1 figure; v2: references added, typos corrected; v3: major improvement of the references; v4: Discussion of short operators is restricted to the case n=1. This restriction does not affect the main results of the paper