局域对称性与对扩展时空的依赖
Local symmetry and the dependence on extended spacetime
AI总结：
本文证明线性化E理论在低能级具有局域对称性，其参数需满足微分条件以限制对扩展时空的依赖，并在Siegel理论（即双场理论）中发现类似限制，同时论证无需对场施加额外条件。
AI中文摘要：
我们证明，线性化的E理论在低能级具有局域对称性，前提是局域对称性的参数满足微分条件，这些条件限制了对扩展时空的依赖。在导致Siegel理论（也称为双场理论）的E理论分解中，我们也发现了参数上的类似限制。它们与在此背景下普遍使用的截面条件不同。我们还证明，如果参数满足类似的非线性约束，Siegel理论的膨胀方程在局域对称性下是不变的。我们认为，没有必要对E理论或Siegel理论的场施加条件。
英文摘要：
We show that linearised E theory possesses a local symmetry at low levels provided the parameters of the local symmetry obey differential conditions that restrict their dependence on the extended spacetime. In the decomposition of E theory that leads to Siegel theory, also known as Double Field theory, we also find the analogous restrictions on the parameters. They are different to the section conditions which are universally used in this context. We also show that the dilaton equation of Siegel theory is invariant under the local symmetry if the parameters satisfy an analogous non-linear constraint on the parameters. We argue that there is no need to impose conditions on the fields of E theory or Siegel theory.
