Non-Geometric T-Duality as Higher Groupoid Bundles with Connections
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2022
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911725514653696 |
|---|---|
| author | Kim, Hyungrok Saemann, Christian |
| author_facet | Kim, Hyungrok Saemann, Christian |
| contents | We propose a description of T-duality between general geometric and non-geometric backgrounds as higher groupoid bundles with connections. Our description extends the previous observation by Nikolaus and Waldorf that the topological aspects of geometric and half-geometric T-dualities can be described in terms of higher geometry. We extend their construction in two ways. First, we endow the higher geometries with adjusted connections, which allow us to discuss explicit formulas for the metric and the Kalb-Ramond field of a T-background. Second, we extend the principal 2-bundles to principal 2-groupoid bundles, which accommodate the scalar fields arising in T-dualities along two directions as well as $Q$-fluxes. Our proposals reproduce key examples from the literature. They are manifestly covariant under the full T-duality group $\mathsf{GO}(n,n;\mathbb{Z})$ and have interesting physical and mathematical implications. Eventually, we also comment on the case of T-duality in the presence of scalar fluxes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_01783 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Non-Geometric T-Duality as Higher Groupoid Bundles with Connections Kim, Hyungrok Saemann, Christian High Energy Physics - Theory Mathematical Physics We propose a description of T-duality between general geometric and non-geometric backgrounds as higher groupoid bundles with connections. Our description extends the previous observation by Nikolaus and Waldorf that the topological aspects of geometric and half-geometric T-dualities can be described in terms of higher geometry. We extend their construction in two ways. First, we endow the higher geometries with adjusted connections, which allow us to discuss explicit formulas for the metric and the Kalb-Ramond field of a T-background. Second, we extend the principal 2-bundles to principal 2-groupoid bundles, which accommodate the scalar fields arising in T-dualities along two directions as well as $Q$-fluxes. Our proposals reproduce key examples from the literature. They are manifestly covariant under the full T-duality group $\mathsf{GO}(n,n;\mathbb{Z})$ and have interesting physical and mathematical implications. Eventually, we also comment on the case of T-duality in the presence of scalar fluxes. |
| title | Non-Geometric T-Duality as Higher Groupoid Bundles with Connections |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2204.01783 |