Strongcoupling expansion of cusp anomaly and gluon amplitudes from quantum open strings in AdS_{5}×S^{5}
Abstract
An important "observable" of planar N=4 SYM theory is the scaling function f(λ) that appears in the anomalous dimension of large spin twist 2 operators and also in the cusp anomaly of lightlike Wilson loop. The nontrivial relation between the anomalous dimension and the Wilson loop interpretations of f(λ) is wellunderstood on the perturbative gauge theory side of the AdS/CFT duality. In the first part of this paper we present the dual stringtheory counterpart of this relation, i.e., the equivalence between the closedstring and the openstring origins of f(λ). We argue that the coefficient of the logS term in the energy of the closed string with large spin S in AdS should be equal to the coefficient in the logarithm of expectation value of the null cusp Wilson loop, to all orders in λ expansion. The reason is that the corresponding minimal surfaces happen to be related by a conformal transformation (and an analytic continuation). As a check, we explicitly compute the leading 1loop string sigma model correction to the cusp Wilson loop, reproducing the same subleading coefficient in f(λ) as found earlier in the spinning closed string case. The same function f(λ) appears also in the resummed form of the 4gluon amplitude as discussed at weak coupling by Bern, Dixon and Smirnov and recently found at the leading order at strong coupling by Alday and Maldacena (AM). Here we attempt to extend the latter approach to a subleading order in λ by computing the IR singular part of the 1loop string correction to the corresponding Tdual Wilson loop. We discuss explicitly the 1cusp case and comment on apparent problems with the dimensional regularization proposal of AM when directly applied order by order in strong coupling (string inverse tension) expansion.
 Publication:

Nuclear Physics B
 Pub Date:
 March 2008
 DOI:
 10.1016/j.nuclphysb.2007.09.005
 arXiv:
 arXiv:0707.4254
 Bibcode:
 2008NuPhB.791...93K
 Keywords:

 11.25.Tq;
 11.15.Me;
 11.25.Mj;
 Gauge/string duality;
 Strongcoupling expansions;
 Compactification and fourdimensional models;
 High Energy Physics  Theory
 EPrint:
 35 pages. v2: minor corrections, references added