Loss of solution in the symmetry improved Phi-derivable expansion scheme

Abstract

We consider the two-loop Phi-derivable approximation for the O(2)-symmetric scalar model, augmented by the symmetry improvement introduced in [A. Pilaftsis and D. Teresi, Nucl. Phys. B874, 594 (2013)], which enforces Goldstone's theorem in the broken phase. Although the corresponding equations admit a solution in the presence of a large enough infrared (IR) regulating scale, we argue that, for smooth ultraviolet (UV) regulators, the solution is lost when the IR scale becomes small enough. Infrared regular solutions exist for certain non-analytic UV regulators, but we argue that these solutions are artifacts which should disappear when the sensitivity to the UV regulator is removed by a renormalization procedure. The loss of solution is observed both at zero and at finite temperature, although it is simpler to identify in the latter case. We also comment on possible ways to cure this problem.

20 pages, 7 figures, uses elsarticle, published version

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Cited by in corpus (9)

• Cosmological phase transitions: from perturbative particle physics to gravitational waves
• Finite temperature spectral functions in the O(N)-model
• Bound state properties from the Functional Renormalisation Group
• The 2PI effective theory at next-to-leading order using the functional renormalization group
• Exact RG Invariance and Symmetry Improved 2PI Effective Potential
• Resummation of Goldstone Infrared Divergences: A Proof to All Orders
• Padé approximants and analytic continuation of Euclidean Phi-derivable approximations
• Renormalization of the 4PI effective action using the functional renormalization group
• Soft symmetry improvement of two particle irreducible effective actions