η -symbols in Exceptional Field Theory
Yuho Sakatani (Department of Physics, Kyoto Prefectural University of Medicine, Kyoto 606-0823, Japa, Fields, Gravity & Strings, CTPU, Institute for Basic Sciences, Seoul 08826, Korea); Shozo Uehara (Department of Physics, Kyoto Prefectural University of Medicine, Kyoto 606-0823, Japa)
We present the universal form of -symbols that can be applied to an arbitrary exceptional field theory (EFT) up to . We then express the -tensor, which governs the gauge algebra of EFT, as a quadratic form of the -symbols. The usual definition of the -tensor strongly depends on the dimension of the compactification torus while it is not the case for our -tensor. Furthermore, using the -symbols, we propose a universal form of the linear section equation. In particular, in the EFT, we explicitly show the equivalence to the known linear section equation.