Six-loop ε expansion of three-dimensional U(n) x U(m) models

We analyze the Landau-Wilson field theory with U(n) x U(m) symmetry which describes the finite-temperature phase transition in QCD in the limit of vanishing quark masses with n = m = N-f flavors and unbroken anomaly at the critical temperature. The six-loop expansions of the renormalization group functions are calculated within the Minimal Subtraction scheme in 4 - epsilon dimensions. The epsilon series for the upper marginal dimensionality n(+)(m, 4 - epsilon) - the key quantity of the theory - are obtained and resummed by means of different approaches. The numbers found are compared with their counterparts obtained earlier within lower perturbative order. In particular, using an increase in the accuracy of numerical results for n(+)(m, 3) by one order of magnitude, we strengthen the conclusions obtained within previous order in perturbation theory about fairness of the inequality n(+)(m, 3) > m. This, in turn, indicates the absence of a stable three-dimensional fixed point for n = m, and as a consequence a first-order kind of finite-temperature phase transition in light QCD. (C) 2022 The Author(s). Published by Elsevier B.V.