Scaling results for isospin charged operators near the QCD conformal window

This work, drawing upon [1], uncovers the leading near-conformal corrections on a cylinder to the scaling dimension of operators with isospin charge 𝑄 defined at the lower boundary of the QCD conformal window. The method involves determining the classical ground state energy of the theory on the cylinder using a semiclassical large charge expansion. In the conformal limit, this energy maps, by state-operator correspondence, into the scaling dimension of the lowest- energy operator carrying a generalised isospin charge 𝑄. We find that the leading near-conformal corrections to the scaling dimension display distinctive 𝑄-dependent scalings, arising from the anomalous dimension of the quark mass operator and the one related to the operator working as a potential for the dilaton that dynamically shifts QCD away from the conformal window.