Six-loop $\epsilon$ expansion of three-dimensional $\text{U}(n)\times \text{U}(m)$ models

Abstract

We analyze the Landau-Wilson field theory with $\text{U}(n)\times \text{U}(m)$ 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 orders and the pseudo-$\epsilon$ analysis of massive six-loop three-dimensional expansions. 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.

References in corpus (4)

• Six-loop $\epsilon$ expansion study of three-dimensional $n$-vector model with cubic anisotropy
• Six-loop beta functions in general scalar theory
• Six-loop $\epsilon$ expansion study of three-dimensional $O(n)\times O(m)$ spin models
• Renormalization group functions of ${\varphi }^4$ theory in the MS-scheme to six loops

Cited by in corpus (4)

• CFTs with $U(m)\times U(n)$ Global Symmetry in 3D and the Chiral Phase Transition of QCD
• Critical behavior of isotropic systems with strong dipole-dipole interaction: three-loop study
• Extrapolation from hypergeometric functions, continued functions and Borel-Leroy transformation; Resummation of perturbative renormalization functions from field theories
• Classifying irreducible fixed points of five scalar fields in perturbation theory