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Structure of large spin expansion of anomalous dimensions at strong coupling

Beccaria, M., Forini, V. ORCID: 0000-0001-9726-1423, Tirziu, A. and Tseytlin, A. A. (2009). Structure of large spin expansion of anomalous dimensions at strong coupling. Nuclear Physics B, 812(1-2), pp. 144-180. doi: 10.1016/j.nuclphysb.2008.12.013

Abstract

The anomalous dimensions of planar N = 4 SYM theory operators like tr (ΦD S + Φ) expanded in large spin S have the asymptotics γ = f ln S + f c + 1 S (f 11 ln S + f 10 ) + ··· ,where f (the universal scaling function or cusp anomaly), f c and f mn are given by power series in the ’t Hooft coupling λ . The subleading coefficients appear to be related by the so-called functional relation and parity (reciprocity) property of the function expressing γ in terms of the conformal spin of the collinear group. Here we study the structure of such large spin expansion at strong coupling via AdS/CFT, i.e. by using the dual description in terms of folded spinning string in AdS 5 . The large spin expansion of the classical string energy happens to have exactly the same structure as that of γ in the perturbative gauge theory. Moreover, the functional relation and the reciprocity constraints on the coefficients are also satisfied. We compute the leading string 1-loop corrections to the coefficients f c , f 11 , f 10 and verify the functional/reciprocity relations at subleading 1 √ λ order. This provides a strong indication that these relations hold not only in weak coupling (gauge-theory) but also in strong coupling (string-theory) perturbative expansions.

Publication Type: Article
Additional Information: © 2008 Elsevier B.V. All rights reserved. This is an open access article published under a Creative Commons license.
Publisher Keywords: String theory, Gauge theory, AdS/CFT correspondence
Departments: School of Mathematics, Computer Science & Engineering
URI: http://openaccess.city.ac.uk/id/eprint/19732
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