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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2507.04091 |
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| _version_ | 1866913161977790464 |
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| author | Pinzul, A. Stern, A. Xu, Chuang |
| author_facet | Pinzul, A. Stern, A. Xu, Chuang |
| contents | In this work, we promote the global $SL(2,\mathbb{R})$ symmetry of the Schwarzian derivative to a local gauge symmetry. To achieve this, we develop a procedure that potentially can be generalized beyond the $SL(2,\mathbb{R})$ case: We first construct a composite field from the fundamental field and its derivative such that it transforms linearly under the group action. Then we write down its gauge-covariant extension and apply standard gauging techniques. Applying this to the fractional linear representation of $SL(2,\mathbb{R})$, we obtain the gauge-invariant analogue of the Schwarzian derivative as a bilinear invariant of covariant derivatives of the composite field. The framework enables a simple construction of Nöther charges associated with the original global symmetry. The gauge-invariant Schwarzian action introduces $SL(2,\mathbb{R})$ gauge potentials, allowing for locally invariant couplings to additional fields, such as fermions. While these potentials can be gauged away on topologically trivial domains, non-trivial topologies (e.g., $S^1$) lead to distinct topological sectors. We mention that in the context of two-dimensional gravity, these sectors could correspond to previously discussed defects in the bulk theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04091 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gauging the Schwarzian Action Pinzul, A. Stern, A. Xu, Chuang Mathematical Physics General Relativity and Quantum Cosmology High Energy Physics - Theory In this work, we promote the global $SL(2,\mathbb{R})$ symmetry of the Schwarzian derivative to a local gauge symmetry. To achieve this, we develop a procedure that potentially can be generalized beyond the $SL(2,\mathbb{R})$ case: We first construct a composite field from the fundamental field and its derivative such that it transforms linearly under the group action. Then we write down its gauge-covariant extension and apply standard gauging techniques. Applying this to the fractional linear representation of $SL(2,\mathbb{R})$, we obtain the gauge-invariant analogue of the Schwarzian derivative as a bilinear invariant of covariant derivatives of the composite field. The framework enables a simple construction of Nöther charges associated with the original global symmetry. The gauge-invariant Schwarzian action introduces $SL(2,\mathbb{R})$ gauge potentials, allowing for locally invariant couplings to additional fields, such as fermions. While these potentials can be gauged away on topologically trivial domains, non-trivial topologies (e.g., $S^1$) lead to distinct topological sectors. We mention that in the context of two-dimensional gravity, these sectors could correspond to previously discussed defects in the bulk theory. |
| title | Gauging the Schwarzian Action |
| topic | Mathematical Physics General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2507.04091 |