Kac-Moody Algebras on Soft Group Manifolds
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915736214044672 |
|---|---|
| author | Campoamor-Stursberg, Rutwig Marrani, Alessio de Traubenberg, Michel Rausch |
| author_facet | Campoamor-Stursberg, Rutwig Marrani, Alessio de Traubenberg, Michel Rausch |
| contents | Within the so-called group geometric approach to (super)gravity and (super)string theories, any compact Lie group manifold $G_{c}$ can be smoothly deformed into a group manifold $G_{c}^{μ}$ (locally diffeomorphic to $G_{c}$ itself), which is `soft', namely, based on a non-left-invariant, intrinsic one-form Vielbein $μ$, which violates the Maurer-Cartan equations and consequently has a non-vanishing associated curvature two-form. Within the framework based on the above deformation (`softening'), we show how to construct an infinite-dimensional (infinite-rank), generalized Kac-Moody (KM) algebra associated to $G_{c}^{μ}$, starting from the generalized KM algebras associated to $G_{c}$. As an application, we consider KM algebras associated to deformed manifolds such as the `soft' circle, the `soft' two-sphere and the `soft' three-sphere. While the generalized KM algebra associated to the deformed circle is trivially isomorphic to its undeformed analogue, and hence not new, the `softening' of the two- and three- sphere includes squashed manifolds (and in particular, the so-called Berger three-sphere) and yields to non-trivial results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15892 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kac-Moody Algebras on Soft Group Manifolds Campoamor-Stursberg, Rutwig Marrani, Alessio de Traubenberg, Michel Rausch High Energy Physics - Theory Mathematical Physics Representation Theory Within the so-called group geometric approach to (super)gravity and (super)string theories, any compact Lie group manifold $G_{c}$ can be smoothly deformed into a group manifold $G_{c}^{μ}$ (locally diffeomorphic to $G_{c}$ itself), which is `soft', namely, based on a non-left-invariant, intrinsic one-form Vielbein $μ$, which violates the Maurer-Cartan equations and consequently has a non-vanishing associated curvature two-form. Within the framework based on the above deformation (`softening'), we show how to construct an infinite-dimensional (infinite-rank), generalized Kac-Moody (KM) algebra associated to $G_{c}^{μ}$, starting from the generalized KM algebras associated to $G_{c}$. As an application, we consider KM algebras associated to deformed manifolds such as the `soft' circle, the `soft' two-sphere and the `soft' three-sphere. While the generalized KM algebra associated to the deformed circle is trivially isomorphic to its undeformed analogue, and hence not new, the `softening' of the two- and three- sphere includes squashed manifolds (and in particular, the so-called Berger three-sphere) and yields to non-trivial results. |
| title | Kac-Moody Algebras on Soft Group Manifolds |
| topic | High Energy Physics - Theory Mathematical Physics Representation Theory |
| url | https://arxiv.org/abs/2501.15892 |