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arXiv · 2501.15892

Kac-Moody Algebras on Soft Group Manifolds

Rutwig Campoamor-Stursberg·Alessio Marrani·Michel Rausch de Traubenberg
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Abstract

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 $G_{c}^{\mu }$ (locally diffeomorphic to $G_{c}$ itself), which is `soft', namely, based on a non-left-invariant, intrinsic one-form Vielbein $\mu $, 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 $G_{c}^{\mu }$, 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.

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Rutwig Campoamor-Stursberg, Alessio Marrani, Michel Rausch de Traubenberg. 2025-01-27. Kac-Moody Algebras on Soft Group Manifolds. https://doi.org/10.1016/j.geomphys.2025.105587

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