Disturbing news about the $d=2+ε$ expansion
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| Format: | Preprint |
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2025
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| author | De Cesare, Fabiana Rychkov, Slava |
| author_facet | De Cesare, Fabiana Rychkov, Slava |
| contents | The $O(N)$ Non-Linear Sigma Model (NLSM) in $d=2+ε$ has long been conjectured to describe the same conformal field theory (CFT) as the Wilson-Fisher (WF) $O(N)$ fixed point obtained from the $λ(ϕ^2)^2$ model in $d=4-ε$. In this work, we put this conjecture into question, building on the recent observation [Jones (2024)] that the NLSM CFT possesses a protected operator with dimension $N-1$, which is instead absent in the WF $O(N)$ CFT. We investigate the possibility of lifting this operator via multiplet recombination - the only known mechanism that could resolve this mismatch while preserving a connection between the two theories. We also explore an alternative scenario in which the NLSM $O(N)$ fixed point in $d=2+ε$ is not continuously connected to the WF $O(N)$ CFT, and instead corresponds to a different universality class. For $N=3$, this could be related to the hedgehog-suppressed critical point, which describes the Néel-VBS phase transition in 3D. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_21611 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Disturbing news about the $d=2+ε$ expansion De Cesare, Fabiana Rychkov, Slava High Energy Physics - Theory Statistical Mechanics Strongly Correlated Electrons The $O(N)$ Non-Linear Sigma Model (NLSM) in $d=2+ε$ has long been conjectured to describe the same conformal field theory (CFT) as the Wilson-Fisher (WF) $O(N)$ fixed point obtained from the $λ(ϕ^2)^2$ model in $d=4-ε$. In this work, we put this conjecture into question, building on the recent observation [Jones (2024)] that the NLSM CFT possesses a protected operator with dimension $N-1$, which is instead absent in the WF $O(N)$ CFT. We investigate the possibility of lifting this operator via multiplet recombination - the only known mechanism that could resolve this mismatch while preserving a connection between the two theories. We also explore an alternative scenario in which the NLSM $O(N)$ fixed point in $d=2+ε$ is not continuously connected to the WF $O(N)$ CFT, and instead corresponds to a different universality class. For $N=3$, this could be related to the hedgehog-suppressed critical point, which describes the Néel-VBS phase transition in 3D. |
| title | Disturbing news about the $d=2+ε$ expansion |
| topic | High Energy Physics - Theory Statistical Mechanics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2505.21611 |