Asymptotically Free Theory with Scale Invariant Thermodynamics

Abstract

A recently developed variational resummation technique, incorporating renormalization group properties consistently, has been shown to solve the scale dependence problem that plagues the evaluation of thermodynamical quantities, e.g., within the framework of approximations such as in the hard-thermal-loop resummed perturbation theory. This method is used in the present work to evaluate thermodynamical quantities within the two-dimensional nonlinear sigma model, which, apart from providing a technically simpler testing ground, shares some common features with Yang-Mills theories, like asymptotic freedom, trace anomaly and the nonperturbative generation of a mass gap. The present application confirms that nonperturbative results can be readily generated solely by considering the lowest-order (quasi-particle) contribution to the thermodynamic effective potential, when this quantity is required to be renormalization group invariant. We also show that when the next-to-leading correction from the method is accounted for, the results indicate convergence, apart from optimally preserving, within the approximations here considered, the sought-after scale invariance.

arXiv comment24 pages, 10 figures. v2: some corrections in a few figures, more explanations on the difference with standard optimized perturbation or hard thermal loop resummation. One reference added. To appear in Phys. Rev. D

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• Chiral Condensate and Spectral Density at full five-loop and partial six-loop orders of Renormalization Group Optimized Perturbation
• Renormalization group improved pressure for hot and dense quark matter
• Renormalization group optimized $\lambda {\varphi }^4$ pressure at next-to-next-to-leading order
• Comparing strange and non-strange quark stars within resummed QCD at NLO