Exact beta function from the holographic loop equation of large-N QCD4

We construct and study a quantum holographic effective action, Gamma(q), whose critical equation implies the holographic loop equation of large-N QCD(4) for planar self-avoiding loops in a certain regularization scheme. We extract from Gamma(q) the exact beta function in the given scheme. For the Wilsonean coupling constant the beta function is exactly one loop and the first coefficient, beta(0), agrees with its value in perturbation theory. For the canonical coupling constant the exact beta function has a NSVZ form and the first two coefficients in powers of the coupling, beta(0) and beta(1), agree with their value in perturbation theory.