Differential Contracting Homotopy in the Linearized 3d Higher-Spin Theory
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914525427531776 |
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| author | Vasiliev, M. A. Vereitin, V. A. |
| author_facet | Vasiliev, M. A. Vereitin, V. A. |
| contents | In this paper, the recently developed differential homotopy approach is applied to the problem of disentangling dynamical and topological fields of the $3d$ higher-spin gauge theory at the linear level. This formalism allows us to reproduce all known disentangling solutions in a unified form, including both the solutions obtained previously within the shifted homotopy approach in \cite{Korybut:2022kdx} and that derived by hand in \cite{Vasiliev:1992ix}, as well as other solutions including those associated with the cohomology of the background covariant derivative $D_0$. Also, within the differential homotopy framework an alternative way of derivation of disentangled equations through a non-conventional solution for the field $S_1$ is suggested. The obtained results are important for further analysis of nonlinear corrections to HS equations in $AdS_3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_11500 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Differential Contracting Homotopy in the Linearized 3d Higher-Spin Theory Vasiliev, M. A. Vereitin, V. A. High Energy Physics - Theory In this paper, the recently developed differential homotopy approach is applied to the problem of disentangling dynamical and topological fields of the $3d$ higher-spin gauge theory at the linear level. This formalism allows us to reproduce all known disentangling solutions in a unified form, including both the solutions obtained previously within the shifted homotopy approach in \cite{Korybut:2022kdx} and that derived by hand in \cite{Vasiliev:1992ix}, as well as other solutions including those associated with the cohomology of the background covariant derivative $D_0$. Also, within the differential homotopy framework an alternative way of derivation of disentangled equations through a non-conventional solution for the field $S_1$ is suggested. The obtained results are important for further analysis of nonlinear corrections to HS equations in $AdS_3$. |
| title | Differential Contracting Homotopy in the Linearized 3d Higher-Spin Theory |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2508.11500 |