Scaling results for charged sectors of near conformal QCD

We provide the leading near conformal corrections on a cylinder to the scaling dimension of the lowest-lying fixed isospin charge Q operators defined at the lower boundary of the quantum chromodynamics conformal window, ΔQ=ΔQ∗+(mσ4πν)2QΔ3B1+(mπ(θ)4πν)4Q23(1-γ)B2+O(mσ4,mπ8,mσ2mπ4). Here, ΔQ/r is the classical ground state energy of the theory on R×Sr3 at fixed isospin charge while ΔQ∗ is the scaling dimension at the leading order in the large charge expansion. In the conformal limit mσ=mπ=0, the state-operator correspondence implies ΔQ=ΔQ∗. The near-conformal corrections are expressed in powers of the dilaton and pion masses in units of the chiral symmetry breaking scale 4πν with the θ-angle dependence encoded directly in the pion mass. The characteristic Q-scaling is dictated by the quark mass operator anomalous dimension γ and the one characterizing the dilaton potential Δ. The coefficients Bi with i=1,2 depend on the geometry of the cylinder and properties of the nearby conformal field theory.