A note on twist two operators in Script N = 4 SYM and Wilson loops in Minkowski signature

Abstract

Recently, the anomalous dimension of twist two operators in N = 4 SYM theory was computed by Gubser, Klebanov and Polyakov in the limit of large 't Hooft coupling using semi-classical rotating strings in AdS 5 . Here we reproduce their results for large angular momentum by using the cusp anomaly of Wilson loops in Minkowski signature also computed within the AdS/CFT correspondence. In our case the anomalous dimension is related to an Euclidean world-sheet whose properties are completely determined by the symmetries of the problem. This gives support to the proposed identification of rotating strings and twist two operators. 1 See [4] for a review and a complete set of references. 2 See also the recent works [7, 8].

Gauge theory webs and surfaces

“…The integrand, a web function, depends on the single invariant scale through the running of the coupling, which for a theory that is conformal in four dimensions agrees with strong-coupling results [12,13,43]. This agreement extends to aspects of closed, polygonal Wilson loops.…”

Gauge-String Dualities and some Applications

“…This gives the prediction that f (g) → 4g at strong coupling. The same result was obtained from studying the cusp anomaly using string theory methods [39]. Furthermore, the semi-classical expansion for the spinning string energy predicts the following correction [34]:…”

Notes on Euclidean Wilson loops and Riemann theta functions

“…It should be noted that a similar property was observed in [28]. In that case, however, the Wilson loops considered were composed of straight light-like segments joining at cusps as the one considered in [7]. Nevertheless, at least in principle, an Euclidean Wilson loop can be considered as a limiting case of a light-like one in the case of an infinite number of cusps.…”

“…In the language we use here they correspond to elliptic functions which appear for genus one g = 1. In the case of Minkowski signature AdS space and in particular light-like lines more is known starting with the light-like cusp [7] and culminating with a large recent activity [8] in relation to scattering amplitudes following [10,11].…”