Boundary Scattering and Non-invertible Symmetries in 1+1 Dimensions
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915236912562176 |
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| author | Shimamori, Soichiro Yamaguchi, Satoshi |
| author_facet | Shimamori, Soichiro Yamaguchi, Satoshi |
| contents | Recent studies by Copetti, Córdova and Komatsu have revealed that when non-invertible symmetries are spontaneously broken, the conventional crossing relation of the S-matrix is modified by the effects of the corresponding topological quantum field theory (TQFT). In this paper, we extend these considerations to $(1+1)$-dimensional quantum field theories (QFTs) with boundaries. In the presence of a boundary, one can define not only the bulk S-matrix but also the boundary S-matrix, which is subject to a consistency condition known as the boundary crossing relation. We show that when the boundary is weakly-symmetric under the non-invertible symmetry, the conventional boundary crossing relation also receives a modification due to the TQFT effects. As a concrete example of the boundary scattering, we analyze kink scattering in the gapped theory obtained from the $Φ_{(1,3)}$-deformation of a minimal model. We explicitly construct the boundary S-matrix that satisfies the Ward-Takahashi identities associated with non-invertible symmetries. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_08375 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Boundary Scattering and Non-invertible Symmetries in 1+1 Dimensions Shimamori, Soichiro Yamaguchi, Satoshi High Energy Physics - Theory Strongly Correlated Electrons Exactly Solvable and Integrable Systems Recent studies by Copetti, Córdova and Komatsu have revealed that when non-invertible symmetries are spontaneously broken, the conventional crossing relation of the S-matrix is modified by the effects of the corresponding topological quantum field theory (TQFT). In this paper, we extend these considerations to $(1+1)$-dimensional quantum field theories (QFTs) with boundaries. In the presence of a boundary, one can define not only the bulk S-matrix but also the boundary S-matrix, which is subject to a consistency condition known as the boundary crossing relation. We show that when the boundary is weakly-symmetric under the non-invertible symmetry, the conventional boundary crossing relation also receives a modification due to the TQFT effects. As a concrete example of the boundary scattering, we analyze kink scattering in the gapped theory obtained from the $Φ_{(1,3)}$-deformation of a minimal model. We explicitly construct the boundary S-matrix that satisfies the Ward-Takahashi identities associated with non-invertible symmetries. |
| title | Boundary Scattering and Non-invertible Symmetries in 1+1 Dimensions |
| topic | High Energy Physics - Theory Strongly Correlated Electrons Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2504.08375 |