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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/2509.18959 |
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| _version_ | 1866915509105065984 |
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| author | Batlle, Carles Gomis, Joaquim |
| author_facet | Batlle, Carles Gomis, Joaquim |
| contents | We discuss a general action for a particle in AdS$_3$ using the non-linear realization framework. Critical sectors are found and characterized in terms of the parameters appearing in the Lagrangian, generalizing the known results for AdS$_3$/SO(2). A study of the dynamics of this system and of the geometrical meaning of the new terms in the action is also undertaken.
Using two chiral copies of the general AdS$_2$ Lagrangian, we obtain an AdS$_3$ Lagrangian which is the same, although expressed in different variables, that the general AdS$_3$ one, and from this one can identify the extra gauge transformations appearing in the critical sectors of the AdS$_3$ theory. A differential equation connecting the AdS$_2 \times$ AdS$_2$ chiral variables to the AdS$_3$ covariant ones is obtained, and it is explicitly solved at first order in the Goldstone bosons associated to boosts and rotations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18959 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A general action for a particle in 2+1 anti-de Sitter space Batlle, Carles Gomis, Joaquim High Energy Physics - Theory Mathematical Physics We discuss a general action for a particle in AdS$_3$ using the non-linear realization framework. Critical sectors are found and characterized in terms of the parameters appearing in the Lagrangian, generalizing the known results for AdS$_3$/SO(2). A study of the dynamics of this system and of the geometrical meaning of the new terms in the action is also undertaken. Using two chiral copies of the general AdS$_2$ Lagrangian, we obtain an AdS$_3$ Lagrangian which is the same, although expressed in different variables, that the general AdS$_3$ one, and from this one can identify the extra gauge transformations appearing in the critical sectors of the AdS$_3$ theory. A differential equation connecting the AdS$_2 \times$ AdS$_2$ chiral variables to the AdS$_3$ covariant ones is obtained, and it is explicitly solved at first order in the Goldstone bosons associated to boosts and rotations. |
| title | A general action for a particle in 2+1 anti-de Sitter space |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2509.18959 |