经典拓扑缺陷的靶空间融合
Target-space fusion of classical topological defects
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中文总结 AI 辅助
该研究提出将拓扑缺陷的经典融合表述为靶空间缺陷数据的约化方法，成功重现已知缺陷并构造新缺陷，为非可逆融合提供经典表现，提供了系统的经典融合计算与新缺陷构造方案。
中文摘要 AI 辅助
σ模型缺陷的经典融合通常通过结合其世界面作用量并消去中间场来实现，但该方法无法系统地确定所得靶空间缺陷及其可能的分支。我们通过将融合表述为靶空间缺陷数据的约化来解决这一问题，内禀二形式的局域下降和联络的全局下降确定了可允许的分支。对于SU(2) WZW模型中保持对称性的双膜和霍普夫纤维T对偶缺陷，该方案重现了已知的双共轭类分支和有限的纤维移位缺陷族。多个分支的出现为非可逆融合提供了经典表现。我们进一步利用该框架构造了TsT和T对偶双共轭缺陷，包括其全局一致性条件，因此该框架提供了一种系统方法，可用于计算经典融合并从已知缺陷构造新缺陷。
英文摘要
Classical fusion of sigma-model defects is commonly approached by combining their worldsheet actions and eliminating the intermediate fields. This procedure, however, does not systematically identify the resulting target-space defect or its possible branches. We address this problem by formulating fusion as a reduction of the target-space defect data. Local descent of the intrinsic two-form and global descent of the connection determine the admissible branches. For symmetry-preserving bi-branes in the $SU(2)$ WZW model and Hopf-fibre T-duality defects, the prescription reproduces the known biconjugacy-class branches and the finite family of fibre-shift defects. The appearance of several branches provides a classical manifestation of non-invertible fusion. We further use the framework to construct TsT and T-dual biconjugacy defects, including their global consistency conditions. It therefore provides a systematic method for computing classical fusion and constructing new defects from known ones.
