$\eta$-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.

41 pages; v2: typos corrected, clarifications added; v3: typos corrected, to appear in PTEP; v4: typos corrected in Eq.(3.65) and Table 1

References in corpus (3)

• Exceptional Field Theory III: E${}_{8(8)}$
• Half-maximal supersymmetry from exceptional field theory
• Branes in Extended Spacetime: Brane Worldvolume Theory Based on Duality Symmetry