Strong-coupling expansion of cusp anomaly and gluon amplitudes from quantum open strings in AdS_5 x S^5

TL;DR

The paper analyzes the strong-coupling expansion of the cusp anomaly and gluon amplitudes in AdS5×S5, showing that the scaling function f(λ) can be captured equivalently by either the spinning closed-string or the null cusp open-string picture. By exploiting a homogeneous scaling limit, the authors demonstrate that quantum fluctuations have constant coefficients, enabling a direct 1-loop comparison that yields the same coefficient a1 in both pictures, explicitly $a_1 = -{3\ln 2\over \pi}$. They extend the analysis to IR structures of gluon amplitudes via a T-dual string description, finding consistent results at 1-loop, but encounter significant issues when implementing Alday–Maldacena’s dimensionally regularized prescription at the quantum level. The work highlights both the robustness of the AdS/CFT correspondence for strong-coupling expansions of f(λ) and the challenges of translating IR regularization schemes from gauge theory to string theory without further refinements.

Abstract

An important ``observable'' of planar N=4 SYM theory is the scaling function f(lambda) that appears in the anomalous dimension of large spin twist 2 operators and also in the cusp anomaly of light-like Wilson loops. The non-trivial relation between the anomalous dimension and the Wilson interpretations of f(lambda) is well-understood on the perturbative gauge theory side of the AdS/CFT duality. In the first part of this paper we present the dual string-theory counterpart of this relation, to all orders in lambda^(-1/2) expansion. As a check, we explicitly compute the leading 1-loop string sigma model correction to the cusp Wilson loop, reproducing the same subleading coefficient in f(lambda) as found earlier in the spinning closed string case. The same function f(lambda) appears also in the resummed form of the 4-gluon 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 this approach to subleading order in lambda^(-1/2) by computing the IR singular part of 1-loop string correction to the corresponding T-dual Wilson loop. We discuss explicitly the 1-cusp case and comment on apparent problems with the dimensional regularization proposal of AM when directly applied order by order in strong coupling (inverse string tension) expansion.