Para-Hermitian Geometry, Dualities and Generalized Flux Backgrounds
Para-Hermitian Geometry, Dualities and Generalized Flux Backgrounds
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准厄米几何、对偶性和广义通量背景
DOI：
10.1002/prop.201800093
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Marotta V
中科院分区：
文献类型：
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作者：
Marotta V
我们综述了一些物理模型，这些模型捕捉到了仿厄米流形上双场理论的主要概念。我们证明了拉格朗日动力系统和哈密顿动力系统的几何理论是准Kähler几何的一个例子，它推广到一个天生几何的自然例子。相应的相空间几何属于自然的几乎准Kähler结构族，我们通过非线性连接将其显式地构造为正则准Kähler结构的形变。我们将这一框架扩展到一类非拉格朗日动力系统，它自然地编码了仿厄米几何中的通量的概念。在这种情况下，我们用D-括号定义的弱可积性来描述通量的出现，并将这种构造推广到任意余切丛，其中我们再现了双场理论的标准广义通量。我们还描述了Drinfel‘d双星的仿厄米几何，这清楚地说明了磁通、D-括号和不同极化之间的相互作用。在Manin三重偏振的Drinfel‘d Double上，左不变的准厄米结构下降到一个双重扭曲的环面，我们用它来说明在准厄米几何中，偏振的变化如何引起不同的通量和弦背景。
We survey physical models which capture the main concepts of double field theory on para‐Hermitian manifolds. We show that the geometric theory of Lagrangian and Hamiltonian dynamical systems is an instance of para‐Kähler geometry which extends to a natural example of a Born geometry. The corresponding phase space geometry belongs to the family of natural almost para‐Kähler structures which we construct explicitly as deformations of the canonical para‐Kähler structure by non‐linear connections. We extend this framework to a class of non‐Lagrangian dynamical systems which naturally encodes the notion of fluxes in para‐Hermitian geometry. In this case we describe the emergence of fluxes in terms of weak integrability defined by the D‐bracket, and we extend the construction to arbitrary cotangent bundles where we reproduce the standard generalized fluxes of double field theory. We also describe the para‐Hermitian geometry of Drinfel'd doubles, which gives an explicit illustration of the interplay between fluxes, D‐brackets and different polarizations. The left‐invariant para‐Hermitian structure on a Drinfel'd double in a Manin triple polarization descends to a doubled twisted torus, which we use to illustrate how changes of polarizations give rise to different fluxes and string backgrounds in para‐Hermitian geometry.