Chern-Simons propagators in AdS$_3$
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917133067223040 |
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| author | Bhattacharya, Jyotirmoy Guria, Anurag Prakash, Shiroman Sharma, Aditya Sharma, Tarun |
| author_facet | Bhattacharya, Jyotirmoy Guria, Anurag Prakash, Shiroman Sharma, Aditya Sharma, Tarun |
| contents | We introduce parity-odd spin-1 harmonic functions in AdS$_3$ and study their properties. We demonstrate that such parity-odd harmonics are related to their parity-even counterparts through the action of a `Chern-Simons operator', which we present as a novelty in this paper. This relation leads to the construction of simultaneous eigen-functions of the Laplacian and the Chern-Simons operators. Subsequently, these harmonic functions are employed to construct propagators in pure abelian Chern-Simons theory as well as Maxwell-Chern-Simons theory in a covariant gauge. We demonstrate the consistency of the Chern-Simons propagator with the expected two-point function of the boundary currents. Our results are built upon the embedding formalism, which we modify suitably to incorporate parity-odd structures. This formalism also readily helps us write down parity odd structures for the propagators of higher-spin fields. Finally, we construct a split representation for the parity-odd harmonic functions, which may be useful to compute Witten diagrams with loops. Our results are expected to be useful in perturbative studies of parity violating QFTs on AdS$_3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07752 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Chern-Simons propagators in AdS$_3$ Bhattacharya, Jyotirmoy Guria, Anurag Prakash, Shiroman Sharma, Aditya Sharma, Tarun High Energy Physics - Theory We introduce parity-odd spin-1 harmonic functions in AdS$_3$ and study their properties. We demonstrate that such parity-odd harmonics are related to their parity-even counterparts through the action of a `Chern-Simons operator', which we present as a novelty in this paper. This relation leads to the construction of simultaneous eigen-functions of the Laplacian and the Chern-Simons operators. Subsequently, these harmonic functions are employed to construct propagators in pure abelian Chern-Simons theory as well as Maxwell-Chern-Simons theory in a covariant gauge. We demonstrate the consistency of the Chern-Simons propagator with the expected two-point function of the boundary currents. Our results are built upon the embedding formalism, which we modify suitably to incorporate parity-odd structures. This formalism also readily helps us write down parity odd structures for the propagators of higher-spin fields. Finally, we construct a split representation for the parity-odd harmonic functions, which may be useful to compute Witten diagrams with loops. Our results are expected to be useful in perturbative studies of parity violating QFTs on AdS$_3$. |
| title | Chern-Simons propagators in AdS$_3$ |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2512.07752 |