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arXiv · 2502.07880

Revisiting the $\phi^6$ Theory in Three Dimensions at Large $N$

Sandra Kvedaraitė·Tom Steudtner·Max Uetrecht
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Abstract

We investigate the $O(N)$--symmetric $\phi^6$ theory in three spacetime dimensions using dimensional regularisation and minimal subtraction. The predictions of other methods are scrutinised in a large-$N$ expansion. We show how the tricritical line of fixed point emerges in a strict $N\to\infty$ limit but argue that it is not a physical manifestation. For the first time in this explicit manner, we compute the effective potential at next-to-leading order in the $1/N$-expansion and discuss its stability. The Bardeen-Moshe-Bander phenomenon is also analysed at next-to-leading order, and we demonstrate that it disappears without breaking the scale invariance spontaneously. Our findings indicate that the UV fixed point found by Pisarski persists at large $N$.

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Sandra Kvedaraitė, Tom Steudtner, Max Uetrecht. 2025-02-11. Revisiting the $\phi^6$ Theory in Three Dimensions at Large $N$. https://doi.org/10.1103/tnh4-7lnv

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