2021/05/24 by U. Aglietti, Matteo Becchetti, Aglietti, Ugo +7
Physics and Astronomy · #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #Black Holes and Theoretical Physics
paper · pdf · doi:10.48550/arxiv.2105.11262
We work out the interplay between lowest-order perturbative computations in the 't Hooft coupling, g2=g2YM N, operator mixing, renormalization-group (RG) improved ultraviolet (UV) asymptotics of leading-order (LO) nonplanar/planar contributions to 2-point correlators, and nonperturbative large-N expansion of perturbatively massless QCD-like theories. As concrete examples, we compute to the lowest perturbative order in SU(N) YM theory the ratios, ri, of LO-nonplanar to planar contributions to the 2-point correlators in the orthogonal basis in the coordinate representation of the gauge-invariant dimension-8 scalar operators and all the twist-2 operators. We demonstrate that -- if (γ0)/(β0) has no LO-nonplanar contribution, with γ0 and β0 the one-loop coefficients of the anomalous-dimension matrix and beta function respectively -- ri actually coincides with the corresponding ratio in the large-N expansion of the RG-improved UV asymptotics of the 2-point correlators, provided that a certain canonical nonresonant diagonal renormalization scheme exists for the corresponding operators. Contrary to the aforementioned scalar operators, for the first 103 twist-2 operators we actually verify the above conditions, and we get the universal value ri=-(1)/(N2). Hence, nonperturbatively such ri must coincide with the UV asymptotics of the ratio of the glueball self-energy loop to the glueball tree contribution to the 2-point correlators above. As a consequence, the universality of ri reflects the universality of the effective coupling in the nonperturbative large-N YM theory for the twist-2 operators in the coordinate representation.