Local E(11)

Understand

We give a method of deriving the field-strengths of all massless and massive maximal supergravity theories in any dimension starting from the Kac-Moody algebra $E_{11}$.

• Considering the subalgebra of $E_{11}$ that acts on the fields in the non-linear realisation as a global symmetry, we show how this is promoted to a gauge symmetry enlarging the algebra by the inclusion of additional generators.
• We show how this works in eleven dimensions, and we call the resulting enlarged algebra $E_{11}^{local}$.
• Torus reduction to $D$ dimensions corresponds to taking a subalgebra of $E_{11}^{local}$, called $E_{11,D}^{local}$, that encodes the full gauge algebra of the corresponding $D$-dimensional massless supergravity.