Target-space fusion of classical topological defects
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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BibTeX
@misc{demulder2026targetspace,
title = {{Target-space fusion of classical topological defects}},
author = {Saskia Demulder and Chuying Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.21121},
eprint = {2608.21121},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.21121},
}
RIS
TY - UNPB
TI - Target-space fusion of classical topological defects
AU - Saskia Demulder
AU - Chuying Wang
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2608.21121
UR - https://arxiv.org/abs/2608.21121
AB - 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.
ER -