Renormalization group flow of $O(N)^3$-invariant general sextic tensor model

Gaetan Bardy; Thomas Krajewski; Thomas Muller; Adrian Tanasa

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arXiv · 2602.17422

Renormalization group flow of $O(N)^3$-invariant general sextic tensor model

Gaetan Bardy·Thomas Krajewski·Thomas Muller·Adrian Tanasa

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Abstract

We compute the beta functions for the $O(N)^3$-invariant general sextic tensor model up to cubic order in the coupling constant, and at leading order in the $1/N$ expansion. Our method is a direct, explicit one, in the sense that we identify the appropriate Feynman graphs, we compute their amplitudes which then allows us to obtain the $β$ functions of the model. We perform these computation considering both a long-range and a short-range propagator, within the dimensional regularization framework. We find three fixed points in the short-range case and a line of fixed points, parameterized by the wheel interaction, in the long-range case. This line of fixed points is identical to the one found in the case of the $U(N)^3$-invariant model. Our result proves that the additional $O(N)^3$-invariant interactions do not modify the long-range fixed point structure of the model.

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Gaetan Bardy, Thomas Krajewski, Thomas Muller, Adrian Tanasa. 2026-09-01. Renormalization group flow of $O(N)^3$-invariant general sextic tensor model. https://arxiv.org/abs/2602.17422

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