Revisiting the $ϕ^6$ Theory in Three Dimensions at Large $N$
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911227210366976 |
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| author | Kvedaraitė, Sandra Steudtner, Tom Uetrecht, Max |
| author_facet | Kvedaraitė, Sandra Steudtner, Tom Uetrecht, Max |
| contents | We investigate the $O(N)$--symmetric $ϕ^6$ 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 $N$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_07880 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Revisiting the $ϕ^6$ Theory in Three Dimensions at Large $N$ Kvedaraitė, Sandra Steudtner, Tom Uetrecht, Max High Energy Physics - Theory Statistical Mechanics High Energy Physics - Phenomenology We investigate the $O(N)$--symmetric $ϕ^6$ 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 $N$. |
| title | Revisiting the $ϕ^6$ Theory in Three Dimensions at Large $N$ |
| topic | High Energy Physics - Theory Statistical Mechanics High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2502.07880 |