论文标题
u-duality和courant代数在特殊领域理论中
U-duality and Courant Algebroid in Exceptional Field Theory
论文作者
论文摘要
在本文中，我们研究了特殊领域理论中U二元性下的现场变换。以$ sl（5）$和$ SO（5,5）$特殊字段理论为例，我们明确表明U-二元转换受相应的Courant代数结构的差分几何形状控制。 $ sl（5）$和$（5,5）$转换指定的字段重新定义可以通过Courant代数锚映射实现。基于$ e_d $ extifialiation Field理论中Courant代数的存在，我们希望Courant代数锚定映射也存在于具有较高维度异常组（例如$ e_6 $ and $ e_7 $）的特殊字段理论中。有趣的是，在特殊领域理论中，可以用courant代数的结构来实现u偶的M2-Brane和M5-Brane。由于在每个特殊的领域理论中，所有相关领域都可以用相同的锚映射，因此整个拉格朗日人都由库兰特代数锚定映射控制。特别是，这是通过扩展的广义几何形状中的u二元映射来实现的，从扩展的捆绑包$ e = tm \oplusλ^2 t^*m \oplusλ^5 t^*m \oplusλ^6 tm $ λ^6 t^*m $在全局$ e_d $对称下。从M理论的角度来看，通过U-Duality以如此全球的方式，courant代数锚定映射的U双二重有效理论是一种预期的。
In this paper, we study the field transformation under U-duality in exceptional field theories. Take $SL(5)$ and $SO(5,5)$ exceptional field theories as examples, we explicitly show that the U-duality transformation is governed by the differential geometry of a corresponding Courant algebroid structure. The field redefinition specified by $SL(5)$ and $SO(5,5)$ transformations can be realized by Courant algebroid anchor mapping. Based on the existence of Courant algebroid in $E_d$ exceptional field theory, we expect that the Courant algebroid anchor mapping also exist in exceptional field theories with higher dimensional exceptional groups, such as $E_6$ and $E_7$. Intriguingly, the U-dual M2-brane and M5-brane can be realized with the same structure of Courant algebroid in exceptional field theory. Since in each exceptional field theory, all the involved fields can be mapped with the same anchor, the full Lagrangian is governed by the Courant algebroid anchor mapping. In particular, this is realized by the U-duality mapping in extended generalised geometry, from the extended bundle $E=TM \oplus Λ^2 T^*M \oplus Λ^5 T^*M\oplus Λ^6 TM$ to the U-dual bundle $E^*=T^*M \oplus Λ^2 TM \oplus Λ^5 TM \oplus Λ^6 T^*M$ under the global $E_d$ symmetry. From M-theory point of view, a U-dual effective theory of M-theory is expected from Courant algebroid anchor mapping in such a global manner via U-duality.
