Gauge/string duality for QCD conformal operators

TL;DR

This paper explores the dual string theory descriptions of QCD conformal operators' anomalous dimensions at large conformal spins, revealing symmetries, integrability, and connections between weak and strong coupling regimes.

Contribution

It establishes a dual string picture for QCD operators' anomalous dimensions, linking weak and strong coupling analyses through integrability and string theory representations.

Findings

Weak coupling spectrum exhibits hidden symmetry due to integrability.

One-loop cusp anomaly is equivalent to a disk partition function in 2D Yang-Mills.

Strong coupling analysis reveals extra degrees of freedom from string junctions.

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.