Gauge/string duality for QCD conformal operators

TL;DR

The paper investigates the renormalization-group evolution of QCD light-cone conformal operators at large Lorentz spin J from both weak and strong coupling perspectives. It reveals a unifying structure: at weak coupling the dilatation operator maps to an integrable SL(2, R) spin chain, while at strong coupling the same anomalous dimensions emerge from classical string dynamics in AdS space, via open-string minimal surfaces and rotating long strings, with string junctions encoding extra degrees of freedom for multi-particle operators. A key bridge is the cusp anomalous dimension, whose universal ln J scaling appears in both regimes, and which is related to a disk partition function of 2D Yang-Mills, enabling a stringy interpretation of the weak-coupling results. The work shows how conformal symmetry, integrability, and gauge/string duality together illuminate the spectrum of multi-particle QCD operators and their growth with spin, hinting at a coherent picture across coupling strengths. These insights advance our understanding of hard QCD observables and offer a framework for connecting perturbative evolution to semiclassical string theory in AdS/CFT.

Abstract

Renormalization group evolution of QCD composite light-cone operators, built from two and more quark and gluon fields, is responsible for the logarithmic scaling violations in diverse physical observables. We analyze spectra of anomalous dimensions of these operators at large conformal spins at weak and strong coupling with the emphasis on the emergence of a dual string picture. The multi-particle spectrum at weak coupling has a hidden symmetry due to integrability of the underlying dilatation operator which drives the evolution. In perturbative regime, we demonstrate the equivalence of the one-loop cusp anomaly to the disk partition function in two-dimensional Yang-Mills theory which admits a string representation. The strong coupling regime for anomalous dimensions is discussed within the two pictures addressed recently, -- minimal surfaces of open strings and rotating long closed strings in AdS background. In the latter case we find that the integrability implies the presence of extra degrees of freedom -- the string junctions. We demonstrate how the analysis of their equations of motion naturally agrees with the spectrum found at weak coupling.

Figures (6)

• Figure 1: Leading Feynman diagram of cylinder topology for a non-local $N$-particle operator in the large-$N_c$ limit in the light-cone gauge when only nearest-neighbour interactions survive (left). The array of $\Pi$-shaped Wilson lines resulting from the figure on the left in the Feynman gauge (right).
• Figure 2: Cusp anomaly in one-loop approximation (left) and its interpretation in radial quantization formalism (right).
• Figure 3: Transition amplitude on a sphere between two points $v_\mu$ and $- v'_\mu$ with $\theta_2-\theta_1=\pi-\theta$ and $\tau_2-\tau_1=\tau$ (left). Classical trajectories which saturate the amplitude are multiple windings around the sphere over principles circles, e.g., $\ell = 2$ trajectories (right), separated from each other for illustration purposes only.
• Figure 4: The minimal surfaces swept by open strings whose ends move along the contour of the Wilson loop. The surface of the Wilson loop in the adjoint representation (left) is a double of the Wilson loop in the fundamental representation (right).
• Figure 5: Baryon string with a junction.