Fusion of Integrable Defects and the Defect $g$-Function
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911700464173056 |
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| author | He, Yang Jiang, Yunfeng Liu, Yuxiao |
| author_facet | He, Yang Jiang, Yunfeng Liu, Yuxiao |
| contents | We study exact defect $g$-functions for integrable line defects in two-dimensional integrable quantum field theory and use them to probe defect fusion. We consider three settings: fusion of purely transmitting topological defects, fusion of non-topological defects with reflection and transmission, and fusion of a defect with an integrable boundary. For topological defects, the separated logarithmic $g$-function is additive, and the fusion limit is controlled by the multiplicative composition of transmission factors. For non-topological defects, separation-dependent phases in the Bethe-Yang equations produce oscillatory finite-size effects, while the fused defect is described by effective reflection and transmission amplitudes. In the Ising examples studied here, fusion involving non-topological defects lowers the finite localized contribution to the entropy, whereas topological defect-boundary fusion leaves it unchanged. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_20688 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fusion of Integrable Defects and the Defect $g$-Function He, Yang Jiang, Yunfeng Liu, Yuxiao High Energy Physics - Theory We study exact defect $g$-functions for integrable line defects in two-dimensional integrable quantum field theory and use them to probe defect fusion. We consider three settings: fusion of purely transmitting topological defects, fusion of non-topological defects with reflection and transmission, and fusion of a defect with an integrable boundary. For topological defects, the separated logarithmic $g$-function is additive, and the fusion limit is controlled by the multiplicative composition of transmission factors. For non-topological defects, separation-dependent phases in the Bethe-Yang equations produce oscillatory finite-size effects, while the fused defect is described by effective reflection and transmission amplitudes. In the Ising examples studied here, fusion involving non-topological defects lowers the finite localized contribution to the entropy, whereas topological defect-boundary fusion leaves it unchanged. |
| title | Fusion of Integrable Defects and the Defect $g$-Function |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2605.20688 |