The canonical symmetry reduction of string backgrounds
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911287247634432 |
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| author | Kennon, Aaron Streets, Jeffrey |
| author_facet | Kennon, Aaron Streets, Jeffrey |
| contents | String backgrounds, defined here as metric connections with skew-symmetric torsion and reduced holonomy, yield generalized Ricci solitons relative to the Lee vector field. By a variational argument using the string action, they are also gradient generalized Ricci solitons relative to a potential function. These two observations combine to yield a canonical symmetry, and in this work we derive fundamental features of the transverse geometry, and rigidity phenomena. We prove in a unified conceptual fashion that the transverse geometry satisfies the string generalized Ricci soliton equations (a simplified Hull-Strominger system) in many settings including almost Hermitian, almost contact, $SU(3)$, $G_2$, and $\mathrm{Spin}(7)$ geometry. We also show that the transverse geometry is always conformally co-closed, with the conformal factor given by the associated soliton potential. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20773 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The canonical symmetry reduction of string backgrounds Kennon, Aaron Streets, Jeffrey Differential Geometry Mathematical Physics String backgrounds, defined here as metric connections with skew-symmetric torsion and reduced holonomy, yield generalized Ricci solitons relative to the Lee vector field. By a variational argument using the string action, they are also gradient generalized Ricci solitons relative to a potential function. These two observations combine to yield a canonical symmetry, and in this work we derive fundamental features of the transverse geometry, and rigidity phenomena. We prove in a unified conceptual fashion that the transverse geometry satisfies the string generalized Ricci soliton equations (a simplified Hull-Strominger system) in many settings including almost Hermitian, almost contact, $SU(3)$, $G_2$, and $\mathrm{Spin}(7)$ geometry. We also show that the transverse geometry is always conformally co-closed, with the conformal factor given by the associated soliton potential. |
| title | The canonical symmetry reduction of string backgrounds |
| topic | Differential Geometry Mathematical Physics |
| url | https://arxiv.org/abs/2511.20773 |