Defect Relative Entropy
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917232595959808 |
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| author | Ghasemi, Mostafa |
| author_facet | Ghasemi, Mostafa |
| contents | We introduce the concept of \textit{defect relative entropy} as a measure of distinguishability within the space of defects. We compute the defect relative entropy for conformal/topological defects, deriving a universal formula in conformal field theories (CFTs) on a circle. This formula reduces to the Kullback-Leibler divergence. Furthermore, we provide a detailed expression of the defect relative entropy for diagonal CFTs with specific topological defect choices, utilizing the theory's modular $\mathcal{S}$ matrix. We also present a general formula for the \textit{ defect sandwiched Rényi relative entropy} and the \textit{defect fidelity}. Through explicit calculations in specific models, including the Ising model, the tricritical Ising model, and the $\widehat{su}(2)_{k}$ WZW model, we have made an intriguing finding: zero defect relative entropy between reduced density matrices associated with certain topological defect. Notably, we introduce the concept of the \textit{defect relative sector}, representing the set of topological defects with zero defect relative entropy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21875 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Defect Relative Entropy Ghasemi, Mostafa High Energy Physics - Theory Statistical Mechanics Mathematical Physics Quantum Physics We introduce the concept of \textit{defect relative entropy} as a measure of distinguishability within the space of defects. We compute the defect relative entropy for conformal/topological defects, deriving a universal formula in conformal field theories (CFTs) on a circle. This formula reduces to the Kullback-Leibler divergence. Furthermore, we provide a detailed expression of the defect relative entropy for diagonal CFTs with specific topological defect choices, utilizing the theory's modular $\mathcal{S}$ matrix. We also present a general formula for the \textit{ defect sandwiched Rényi relative entropy} and the \textit{defect fidelity}. Through explicit calculations in specific models, including the Ising model, the tricritical Ising model, and the $\widehat{su}(2)_{k}$ WZW model, we have made an intriguing finding: zero defect relative entropy between reduced density matrices associated with certain topological defect. Notably, we introduce the concept of the \textit{defect relative sector}, representing the set of topological defects with zero defect relative entropy. |
| title | Defect Relative Entropy |
| topic | High Energy Physics - Theory Statistical Mechanics Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2601.21875 |