Defect Relative Entropy

• URL: http://arxiv.org/abs/2601.21875v1
• Date: Thu, 29 Jan 2026 15:40:51 GMT
• Title: Defect Relative Entropy
• Authors: Mostafa Ghasemi,
• Abstract summary: We introduce the concept of textitdefect relative entropy as a measure of distinguishability within the space of defects.<n>We compute the defect relative entropy for conformal/topological defects, deriving a universal formula in conformal field theories (CFTs) on a circle.<n>We provide a detailed expression of the defect relative entropy for diagonal CFTs with specific topological defect choices.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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