Critical scaling in the large-$N$ $O(N)$ model in higher dimensions and its possible connection to quantum gravity

Abstract

The critical scaling of the large-$N$ $O(N)$ model in higher dimensions using the exact renormalization group equations has been studied, motivated by the recently found non-trivial fixed point in $4<d<6$ dimensions with metastable critical potential. Particular attention is paid to the case of $d=5$ where the scaling exponent $\nu$ has the value $1/3$, which coincides with the scaling exponent of quantum gravity in one fewer dimensions. Convincing results show that this relation could be generalized to arbitrary number of dimensions above five. Some aspects of AdS/CFT correspondence are also discussed.

the section about quantum gravity is improved; Appendix added; new references added; matches PRD version

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• ${\varphi }^3$ theory with $F_4$ flavor symmetry in $6-2\epsilon$ dimensions: 3-loop renormalization and conformal bootstrap
• Critical $O(2)$ field theory near six dimensions beyond one loop
• On Large N Expansion of the Sphere Free Energy
• AdS/CFT in Fractional Dimension and Higher Spin Gravity at One Loop
• Higher Derivative Gauge theory in $d=6$ and the $\mathbb{C}{\mathbb{P}}^{(N_f-1)}$ NLSM
• Sphere free energy of scalar field theories with cubic interactions
• $F_4$ symmetric ${\varphi }^3$ theory at four loops