eta-symbols in exceptional field theory

Abstract

We present the universal form of eta-symbols that can be applied to an arbitrary E-d(d) exceptional field theory (EFT) up to d = 7. We then express the Y-tensor, which governs the gauge algebra of EFT, as a quadratic form of the eta-symbols. The usual definition of the Y-tensor strongly depends on the dimension of the compactification torus while it is not the case for our Y-tensor. Furthermore, using the eta-symbols, we propose a universal form of the linear section equation. In particular, in the SL(5) EFT, we explicitly show the equivalence to the known linear section equation. © The Author(s) 2017. Published by Oxford University Press on behalf of the Physical Society of Japan.