Possible large-N fixed-points and naturalness for O(N) scalar fields

TL;DR

This paper explores large-N fixed points in 4d O(N) scalar models using scale invariance to achieve controlled UV behavior and naturally light scalars, revealing a line of non-trivial fixed points and phase structures.

Contribution

It introduces a novel approach to find non-trivial UV fixed points in 4d O(N) models via scale invariance and large-N limit, with detailed analysis of phases and excitations.

Findings

Identifies a line of non-trivial UV fixed points in large-N limit.

Shows scale invariance of the effective action at non-zero hbar.

Derives properties of light excitations and phase transitions.

Abstract

We try to use scale-invariance and the large-N limit to find a non-trivial 4d O(N) scalar field model with controlled UV behavior and naturally light scalar excitations. The principle is to fix interactions by requiring the effective action for space-time dependent background fields to be finite and scale-invariant when regulators are removed. We find a line of non-trivial UV fixed-points in the large-N limit, parameterized by a dimensionless coupling. They reduce to classical la phi^4 theory when hbar -> 0. For hbar non-zero, neither action nor measure is scale-invariant, but the effective action is. Scale invariance makes it natural to set a mass deformation to zero. The model has phases where O(N) invariance is unbroken or spontaneously broken. Masses of the lightest excitations above the unbroken vacuum are found. We derive a non-linear equation for oscillations about the broken vacuum. The interaction potential is shown to have a locality property at large-N. In 3d, our construction reduces to the line of large-N fixed-points in |phi|^6 theory.