论文标题
$ \ mathbb {cp}^n $的可集成变形和广义的kaehler几何形状
Integrable deformation of $\mathbb{CP}^n$ and generalised Kaehler geometry
论文作者
论文摘要
我们基于Arxiv：1912.11036的结果，用于通用商空间上的通用帧字段，并研究了$ \ Mathbb {cp}^n $的可集成变形。特别是，我们展示了当主要手性模型的目标空间是一个复杂的投影空间时，如何原理引入两参数变形。但是，可以根据我们进行的彻底整合性分析所产生的结果来清除第二个参数，我们可以明确构建该参数。我们还阐明了如何将变形的目标空间视为广义的kaehler的实例，或者是同等的双 - 热数几何形状。在这方面，我们找到了$ \ mathbb {cp}^n $的纯旋转器的通用形式，以及针对$ n = 1,2 $的广义kaehler潜力的显式表达式。
We build on the results of arXiv:1912.11036 for generalised frame fields on generalised quotient spaces and study integrable deformations for $\mathbb{CP}^n$. In particular we show how, when the target space of the Principal Chiral Model is a complex projective space, a two-parameter deformation can be introduced in principle. The second parameter can however be removed via a diffeomorphism, which we construct explicitly, in accordance with the results stemming from a thorough integrability analysis we carry out. We also elucidate how the deformed target space can be seen as an instance of generalised Kaehler, or equivalently bi-Hermitian, geometry. In this respect, we find the generic form of the pure spinors for $\mathbb{CP}^n$ and the explicit expression for the generalised Kaehler potential for $n=1,2$.
