Localized RG flows on composite defects and $\mathcal{C}$-theorem
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| Format: | Preprint |
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2024
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| _version_ | 1866918192488644608 |
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| author | Ge, Dongsheng Nishioka, Tatsuma Shimamori, Soichiro |
| author_facet | Ge, Dongsheng Nishioka, Tatsuma Shimamori, Soichiro |
| contents | We consider a composite defect system where a lower-dimensional defect (sub-defect) is embedded to a higher-dimensional one, and examine renormalization group (RG) flows localized on the defect. A composite defect is constructed in the $(3-ε)$-dimensional free $\text{O}(N)$ vector model with line and surface interactions by triggering localized RG flows to non-trivial IR fixed points. Focusing on the case where the symmetry group $\text{O}(N)$ is broken to a subgroup $\text{O}(m)\times\text{O}(N-m)$ on the line defect, there is an $\text{O}(N)$ symmetric fixed point for all $N$, while two additional $\text{O}(N)$ symmetry breaking ones appear for $N\ge 23$. We also examine a $\mathcal{C}$-theorem for localized RG flows along the sub-defect and show that the $\mathcal{C}$-theorem holds in our model by perturbative calculations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_04428 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Localized RG flows on composite defects and $\mathcal{C}$-theorem Ge, Dongsheng Nishioka, Tatsuma Shimamori, Soichiro High Energy Physics - Theory Statistical Mechanics Strongly Correlated Electrons We consider a composite defect system where a lower-dimensional defect (sub-defect) is embedded to a higher-dimensional one, and examine renormalization group (RG) flows localized on the defect. A composite defect is constructed in the $(3-ε)$-dimensional free $\text{O}(N)$ vector model with line and surface interactions by triggering localized RG flows to non-trivial IR fixed points. Focusing on the case where the symmetry group $\text{O}(N)$ is broken to a subgroup $\text{O}(m)\times\text{O}(N-m)$ on the line defect, there is an $\text{O}(N)$ symmetric fixed point for all $N$, while two additional $\text{O}(N)$ symmetry breaking ones appear for $N\ge 23$. We also examine a $\mathcal{C}$-theorem for localized RG flows along the sub-defect and show that the $\mathcal{C}$-theorem holds in our model by perturbative calculations. |
| title | Localized RG flows on composite defects and $\mathcal{C}$-theorem |
| topic | High Energy Physics - Theory Statistical Mechanics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2408.04428 |