Are there scaling solutions in the O(N)-models for large N in d>4?

Abstract

There have been some speculations about the existence of critical unitary O(N)-invariant scalar field theories in dimensions 4<d<6 and for large N. Using the functional renormalization group equation, we show that in the lowest order of the derivative expansion, and assuming that the anomalous dimension vanishes for large $N$, the corresponding critical potentials are either unbounded from below or singular for some finite value of the field.

arXiv comment5 pages, 4 figures, expanded introduction, in press on PRD

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Cited by in corpus (22)

• The nonperturbative functional renormalization group and its applications
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• Global solutions of functional fixed point equations via pseudo-spectral methods
• Critical exponents of O(N) models in fractional dimensions
• Bootstrapping Mixed Correlators in the Five Dimensional Critical O(N) Models
• Solving functional flow equations with pseudo-spectral methods
• Towards conditions for black-hole singularity-resolution in asymptotically safe quantum gravity
• Cosmological bounds on the field content of asymptotically safe gravity-matter models
• Lee-Yang model from the functional renormalization group
• Global Wilson-Fisher fixed points
• Critical O(N) models above four dimensions: Small-N solutions and stability
• Fixed points and the spontaneous breaking of scale invariance
• Critical $O(N)$ models in the complex field plane
• Scaling and superscaling solutions from the functional renormalization group
• Vanishing Beta Function curves from the Functional Renormalisation Group
• Nonabelian Higgs models: paving the way for asymptotic freedom
• Phase transitions in TGFT: Functional renormalization group in the cyclic-melonic potential approximation and equivalence to O$(N)$ models
• Scaling solutions in the derivative expansion
• More on the cubic versus quartic interaction equivalence in the $O(N)$ model
• Critical scaling in the large-$N$ $O(N)$ model in higher dimensions and its possible connection to quantum gravity
• Critical Behavior and Dimension Crossover of Pion Superfluidity
• Critical $O(2)$ and $O(3)$ ${\varphi }^4$ theories near six dimensions