Kaluza‐Klein Theory states that a metric on the total space of a principal bundle , if it is invariant under the principal action of P, naturally reduces to a metric together with a gauge field on the base manifold M. We propose a generalization of this Kaluza‐Klein principle to higher principal bundles and higher gauge fields. For the particular case of the abelian gerbe of Kalb‐Ramond field, this Higher Kaluza‐Klein geometry provides a natural global formulation for Double Field Theory (DFT). In this framework the doubled space is the total space of a higher principal bundle and the invariance under its higher principal action is exactly a global formulation of the familiar strong constraint. The patching problem of DFT is naturally solved by gluing the doubled space with a higher group of symmetries in a higher category. Locally we recover the familiar picture of an ordinary para‐Hermitian manifold equipped with Born geometry. Infinitesimally we recover the familiar picture of a higher Courant algebroid twisted by a gerbe (also known as Extended Riemannian Geometry). As first application we show that on a torus‐compactified spacetime the Higher Kaluza‐Klein reduction gives automatically rise to abelian T‐duality, while on a general principal bundle it gives rise to non‐abelian T‐duality. As final application we define a natural notion of Higher Kaluza‐Klein monopole by directly generalizing the ordinary Gross‐Perry one. Then we show that under Higher Kaluza‐Klein reduction, this monopole is exactly the NS5‐brane on a 10d spacetime. If, instead, we smear it along a compactified direction we recover the usual DFT monopole on a 9d spacetime.

中文翻译：

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全局双场理论是更高的Kaluza-Klein理论

Kaluza-Klein理论指出，主束总空间上的度量（如果在P的主作用下不变）自然会减少为一个度量，并与基础歧管M上的标距场一起。我们建议将此Kaluza-Klein原理推广到更高的主束和更高的规范场。对于Kalb-Ramond场的阿贝尔格贝人的特殊情况，这种较高的Kaluza-Klein几何形状为Double Field Theory（DFT）提供了自然的全局公式。在此框架中，加倍空间是较高主体束的总空间，并且在其较高主体作用下的不变性正是熟悉的强约束的整体表述。DFT的修补问题自然可以通过在较高类别中以较高的一组对称性胶合双重空间来解决。在本地，我们恢复了熟悉的具有Born几何形状的普通准Hermitian流形的图像。无限地，我们恢复了被gerbe扭曲的高级Courant代数的熟悉图片（也称为扩展Riemannian几何）。作为第一个应用，我们显示了在圆环紧凑的时空上，较高的Kaluza-Klein减少量会自动引起阿贝尔T-对偶性，而在一般主体束上，它会引起非阿贝尔T-对偶性。作为最终应用，我们通过直接推广普通的Gross-Perry来定义高Kaluza-Klein单极的自然概念。然后我们证明，在更高的Kaluza-Klein还原下，该单极子恰好是10 作为最终应用，我们通过直接推广普通的Gross-Perry来定义高Kaluza-Klein单极的自然概念。然后我们证明，在更高的Kaluza-Klein还原下，该单极子恰好是10 作为最终应用，我们通过直接推广普通的Gross-Perry来定义高Kaluza-Klein单极的自然概念。然后我们证明，在更高的Kaluza-Klein还原下，该单极子恰好是10d时空。相反，如果我们沿压缩方向涂抹它，那么我们将在9 d 时空上恢复通常的DFT单极子。