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Classical/quantum integrability in AdS/CFT
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Theoretical Physics, Theoretical Physics.
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Theoretical Physics, Theoretical Physics.
2004 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, Vol. 05, 024- p.Article in journal (Refereed) Published
Abstract [en]

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 = 4 super Yang-Mills and the energy of their dual semiclassical string states in AdS5 × S5. 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.

Place, publisher, year, edition, pages
2004. Vol. 05, 024- p.
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:uu:diva-21049DOI: 10.1088/1126-6708/2004/05/024OAI: oai:DiVA.org:uu-21049DiVA: diva2:48822
Available from: 2006-12-14 Created: 2006-12-14 Last updated: 2017-12-08Bibliographically approved

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Publisher's full texthttp://arxiv.org/abs/hep-th/0402207

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Minahan, Joseph A.Zarembo, Konstantin

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