QCD β -function on the string worldsheet

Abstract

We consider confining strings in pure gluodynamics and its extensions with adjoint (s)quarks. We argue that there is a direct map between the set of bulk fields and the worldsheet degrees of freedom. This suggests a close link between the worldsheet S-matrix and parton scattering amplitudes. We report an amusing relation between the Polchinski-Strominger amplitude responsible for the breakdown of integrability on the string worldsheet and the Yang-Mills β-function b0=Dcr-Dph6. Here b0=11/3 is the one-loop β-function coefficient in the pure Yang-Mills theory, Dcr=26 is the critical dimension of bosonic strings and Dph=4 is the dimensionality of the physical space-time we live in. A natural extension of this relation continues to hold in the presence of adjoint (s)quarks, connecting two of the most celebrated anomalies - the scale anomaly in quantum chromodynamics (QCD) and the Weyl anomaly in string theory.