Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-02-26
JHEP 0405 (2004) 024
Physics
High Energy Physics
High Energy Physics - Theory
49 pages, 5 figures, LaTeX; v2: complete proof of the two-loop equivalence between the sigma model and the gauge theory is add
Scientific paper
10.1088/1126-6708/2004/05/024
We discuss the AdS/CFT duality from the perspective of integrable systems and establish a direct relationship between the dimension of single trace local operators composed of two types of scalar fields in N=4 super Yang-Mills and the energy of their dual semiclassical string states in AdS(5) X S(5). The anomalous dimensions can be computed using a set of Bethe equations, which for ``long'' operators reduces to a Riemann-Hilbert problem. We develop a unified approach to the long wavelength Bethe equations, the classical ferromagnet and the classical string solutions in the SU(2) sector and present a general solution, governed by complex curves endowed with meromorphic differentials with integer periods. Using this solution we compute the anomalous dimensions of these long operators up to two loops and demonstrate that they agree with string-theory predictions.
Kazakov Vladimir A.
Marshakov Andrei
Minahan Joseph A.
Zarembo Konstantin
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