Target-space fusion of classical topological defects

Saskia Demulder; Chuying Wang

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arXiv · 2608.21121

Target-space fusion of classical topological defects

Saskia Demulder·Chuying Wang

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Abstract

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.

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Saskia Demulder, Chuying Wang. 2026-08-21. Target-space fusion of classical topological defects. https://arxiv.org/abs/2608.21121

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