arXiv 2102.031672021-02hep-thmath-phmath.MP

迈向T对偶的涌现引力

Towards a T-dual Emergent Gravity

Mathematical Institute, University of Bonn（波恩大学数学研究所）；Dept. of Physics, AppLied Sciences Cluster School of Advanced Engineering UPES（UPES高等工程学院应用科学集群物理系）；Department of Physics and Astrophysics University of Delhi（德里大学物理与天体物理系）

Daniel Bermudez, Raju Roychowdhury

备注：: 32 pages, 2 figures, Revised published version
发表信息：: Fortschritte der Physik 2026; 74:e70141
DOI：: 10.1002/prop.70141

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AI总结：

该研究在广义几何框架下统一涌现引力与拓扑T对偶，构造了主环丛的T对偶涌现引力，建立了两者间的精确数学对应，明确广义几何是T对偶协变涌现引力的自然框架。

摘要：

涌现引力为非对易U(1)规范理论提供了几何实现，其中辛结构的规范场形变通过达布定理被微分同胚吸收，进而产生有效黎曼度量。另一方面，拓扑T对偶将具有不同几何和通量数据的主环丛关联起来，这些主环丛对应的σ模型在物理上等价。我们在广义几何框架下统一这两种构造，通过在精确Courant algebroid上用广义度量表述涌现引力。在该描述中，Seiberg-Witten映射被自然解释为作用于平坦背景的B变换与θ变换的复合。利用Courant algebroid的Gualtieri-Cavalcanti同构，我们为主环丛构造了T对偶涌现引力的概念，并推导了对应的对偶广义度量。对于H通量为零的平坦背景，我们证明T对偶广义度量再次具有涌现引力解释，这由一个交换图编码，其中T对偶交换了生成涌现度量的变换顺序。对于一般的二维环纤维化，我们得到了对偶广义度量的显式表达式，并证明对偶背景通常带有非平凡的H通量，这阻碍了涌现引力的传统辛形式表述，促使将其扩展到非精确Courant algebroid。这些结果在涌现引力与拓扑T对偶之间建立了精确的数学对应关系，并确定广义几何是几何和通量背景下T对偶协变涌现引力表述的自然框架。

英文摘要：

Emergent gravity provides a geometric realization of noncommutative U(1) gauge theory, in which gauge-field deformations of a symplectic structure are absorbed by diffeomorphisms through the Darboux theorem, giving rise to an effective Riemannian metric. Independently, topological T-duality relates principal torus bundles with different geometric and flux data whose associated sigma models are physically equivalent. We unify these two constructions within the framework of generalized geometry by formulating emergent gravity in terms of generalized metrics on exact Courant algebroids. In this description, the Seiberg-Witten map is naturally interpreted as a composition of B-transformations and theta-transformations acting on a flat background. Using the Gualtieri-Cavalcanti isomorphism of Courant algebroids, we construct a notion of T-dual emergent gravity for principal torus bundles and derive the corresponding dual generalized metrics. For flat backgrounds with vanishing H-flux, we show that the T-dual generalized metric again admits an emergent gravity interpretation, encoded by a commutative diagram in which T-duality exchanges the order of the transformations generating the emergent metric. For general two-torus fibrations, we obtain explicit expressions for the dual generalized metric and demonstrate that the dual background generically carries nontrivial H-flux, obstructing a conventional symplectic formulation of emergent gravity and motivating an extension to non-exact Courant algebroids. These results establish a precise mathematical correspondence between emergent gravity and topological T-duality, and identify generalized geometry as the natural framework for a T-duality-covariant formulation of emergent gravity in both geometric and flux backgrounds.

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