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.