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arXiv · 0904.4799

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

Govind S. Krishnaswami
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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.

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Govind S. Krishnaswami. 2009-08-15. Possible large-N fixed-points and naturalness for O(N) scalar fields. https://doi.org/10.1088/1751-8113%2F42%2F34%2F345403

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