E11 and the non-linear dual graviton

Abstract

The non-linear duality relation between the gravity and dual gravity fields are found in E theory by carrying out $E_{11}$ variations of previously found duality relations. We also find the dual graviton equation of motion up to the addition of some very specific terms whose coefficients are not determined. Using the calculations in this paper this ambiguity was resolved in reference [15] where the full non-linear dual gravity equation was found. As a result the equations of motion in E theory have now been found at the full non-linear level up to, and including, level three, which contains the dual graviton field. When truncated to contain fields at levels three and less, and the spacetime is restricted to be the familiar eleven dimensional space time, the equations are equivalent to those of eleven dimensional supergravity.

The discussion on the dual graviton equation is changed to make it clear that this equation was only derived up to certain very specific terms in the first version of this paper. The complete dual graviton equation of motion has now been given in reference [15]

References in corpus (7)

• E11 in 11D
• E11 must be a symmetry of strings and branes
• Generalised Space-time and Gauge Transformations
• E11, Romans theory and higher level duality relations
• On the different formulations of the E11 equations of motion
• The non-linear dual gravity equation of motion in eleven dimensions
• Dual gravity and E11

Cited by in corpus (6)

• A master exceptional field theory
• A note on the double dual graviton
• The non-linear dual gravity equation of motion in eleven dimensions
• Gravity, Dual Gravity and A1+++
• Unfolding $E_{11}$
• Duality Anomalies in Linearized Gravity