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

TL;DR

This paper investigates the critical scaling behavior of the large-$N$ $O(N)$ model in higher dimensions, revealing a potential connection to quantum gravity and discussing implications for AdS/CFT correspondence.

Contribution

It demonstrates the existence of non-trivial fixed points in higher dimensions and explores their possible link to quantum gravity phenomena.

Findings

Critical exponent $ u=1/3$ in 5D matches quantum gravity scaling

Non-trivial fixed points found in dimensions 4<d<6

Potential generalization of gravity connection to higher dimensions

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.