Scaling results for charged sectors of near conformal QCD
Jahmall Bersini (Kavli IPMU (WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan); Alessandra D’Alise (INFN sezione di Napoli, via Cintia, 80126 Napoli, Italy, Department of Physics E. Pancini, Università di Napoli Federico II, via Cintia, 80126 Napoli, Italy, Quantum Theory Center (ℏQTC) at IMADA and D-IAS, Southern Denmark University, Campusvej 55, 5230 Odense M, Denmark); Clelia Gambardella (Scuola Superiore Meridionale, Largo S. Marcellino, 10, 80138 Napoli NA, Italy, INFN sezione di Napoli, via Cintia, 80126 Napoli, Italy, Quantum Theory Center (ℏQTC) at IMADA and D-IAS, Southern Denmark University, Campusvej 55, 5230 Odense M, Denmark); Francesco Sannino (Scuola Superiore Meridionale, Largo S. Marcellino, 10, 80138 Napoli NA, Italy, INFN sezione di Napoli, via Cintia, 80126 Napoli, Italy, Department of Physics E. Pancini, Università di Napoli Federico II, via Cintia, 80126 Napoli, Italy, Quantum Theory Center (ℏQTC) at IMADA and D-IAS, Southern Denmark University, Campusvej 55, 5230 Odense M, Denmark)
We provide the leading near conformal corrections on a cylinder to the scaling dimension of the lowest-lying fixed isospin charge operators defined at the lower boundary of the quantum chromodynamics conformal window, Here, is the classical ground state energy of the theory on at fixed isospin charge while is the scaling dimension at the leading order in the large charge expansion. In the conformal limit , the state-operator correspondence implies . The near-conformal corrections are expressed in powers of the dilaton and pion masses in units of the chiral symmetry breaking scale with the -angle dependence encoded directly in the pion mass. The characteristic -scaling is dictated by the quark mass operator anomalous dimension and the one characterizing the dilaton potential . The coefficients with depend on the geometry of the cylinder and properties of the nearby conformal field theory.