We give a covariant realization of the doubled sigma-model formulation of duality-symmetric string theory within the general framework of para-Hermitian geometry. We define a notion of generalized metric on a para-Hermitian manifold and discuss its relation to Born geometry. We show that a Born geometry uniquely defines a worldsheet sigma-model with a para-Hermitian target space, and we describe its Lie algebroid gauging as a means of recovering the conventional sigma-model description of a physical string background as the leaf space of a foliated para-Hermitian manifold. Applying the Kotov–Strobl gauging leads to a generalized notion of T-duality when combined with transformations that act on Born geometries. We obtain a geometric interpretation of the self-duality constraint that halves the degrees of freedom in doubled sigma-models, and we give geometric characterizations of non-geometric string backgrounds in this setting. We illustrate our formalism with detailed worldsheet descriptions of closed string phase spaces, of doubled groups where our notion of generalized T-duality includes non-abelian T-duality, and of doubled nilmanifolds.

中文翻译：

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准厄米流形和广义 T 对偶的 Born sigma 模型

我们在准厄米几何的一般框架内给出了对偶对称弦理论的双重 sigma 模型公式的协变实现。我们在 para-Hermitian 流形上定义了广义度量的概念，并讨论了它与 Born 几何的关系。我们证明了 Born 几何唯一地定义了一个具有准厄米目标空间的 worldsheet sigma 模型，并且我们将其李代数测量描述为一种将物理字符串背景的传统 sigma 模型描述恢复为叶空间的方法叶状的准厄米流形。当结合作用于 Born 几何的变换时，应用 Kotov-Strobl 测量会导致 T 对偶的广义概念。我们获得了自对偶约束的几何解释，它将双 sigma 模型中的自由度减半，我们在这个设置中给出了非几何弦背景的几何特征。我们用详细的世界表描述来说明我们的形式主义，其中我们的广义 T 对偶概念包括非阿贝尔 T 对偶和倍尼流形。