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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.22318 |
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| _version_ | 1866917195473223680 |
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| author | Guan, Yuepeng Pawlowski, Jan M. Yamada, Masatoshi |
| author_facet | Guan, Yuepeng Pawlowski, Jan M. Yamada, Masatoshi |
| contents | We study topological properties of a quantum mechanical system with $U(1)$-symmetry within the functional renormalisation group (fRG) approach. These properties include the vacuum energy structure and the topological susceptibility. Our approach works with a complexification of the flow equation, and specifically we embed the original symmetry into the complex plane, $U(1)\rightarrow \mathbb{C}$. We compute the effective potential of a given topological sector by restricting ourselves to field configurations with a given generalised non-trivial Chern-Simons numbers. The full potential is directly constructed from these sector potentials. Our results compare well with the benchmark results obtained from solving the corresponding Schrödinger equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_22318 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $θ$-vacuum from functional renormalisation Guan, Yuepeng Pawlowski, Jan M. Yamada, Masatoshi High Energy Physics - Theory High Energy Physics - Phenomenology Quantum Physics We study topological properties of a quantum mechanical system with $U(1)$-symmetry within the functional renormalisation group (fRG) approach. These properties include the vacuum energy structure and the topological susceptibility. Our approach works with a complexification of the flow equation, and specifically we embed the original symmetry into the complex plane, $U(1)\rightarrow \mathbb{C}$. We compute the effective potential of a given topological sector by restricting ourselves to field configurations with a given generalised non-trivial Chern-Simons numbers. The full potential is directly constructed from these sector potentials. Our results compare well with the benchmark results obtained from solving the corresponding Schrödinger equation. |
| title | The $θ$-vacuum from functional renormalisation |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology Quantum Physics |
| url | https://arxiv.org/abs/2507.22318 |