The QCD $\beta$-function On The String Worldsheet

Understand

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 $\beta$-function \[ b_0={D_{cr}-D_{ph}\over 6}\;.