The generalized metric is a T-duality covariant symmetric matrix constructed from the metric and two-form gauge field and arises in generalized geometry. We view it here as a metric on the doubled spacetime and use it to give a simple formulation with manifest T-duality of the double field theory that describes the massless sector of closed strings. The gauge transformations are written in terms of a generalized Lie derivative whose commutator algebra is defined by a double field theory extension of the Courant bracket.

Generalized metric formulation of double field theory

We argue that 11-dimensional supergravity can be described by a nonlinear realization based on the group E11. This requires a formulation of 11-dimensional supergravity in which the gravitational degrees of freedom are described by two fields which are related by duality. We show the existence of such a description of gravity.

https://iopscience.iop.org/article/10.1088/0264-9381/18/21/305/pdf

E(11) and M theory

Inverse Higgs effect in nonlinear realizations

E11, SL(32) and central charges

We reformulate eleven-dimensional supergravity, including fermions, in terms of generalised geometry, for spacetimes that are warped products of Minkowski space with a d-dimensional manifold M with d ≤ 7. The reformulation has an E
 d(d) × ℝ+ structure group and it has a local $ {{\widetilde{H}}_d} $
 symmetry, where $ {{\widetilde{H}}_d} $
 is the double cover of the maximally compact subgroup of E
 d(d). The bosonic degrees for freedom unify into a generalised metric, and, defining the generalisked analogue D of the Levi-Civita connection, one finds that the corresponding equations of motion are the vanishing of the generalised Ricci tensor. To leading order, we show that the fermionic equations of motion, action and supersymmetry variations can all be written in terms of D. Although we will not give the detailed decompositions, this reformulation is equally applicable to type IIA or IIB supergravity restricted to a (d − 1)-dimensional manifold. For completeness we give explicit expressions in terms of $ {{\widetilde{H}}_4} $
 = Spin(5) and $ {{\widetilde{H}}_7} $
 = SU(8) representations for d = 4 and d = 7.

/pdf/supergravity-as-generalised-geometry-ii-e-d-d-times-mathbb-r-41a4k5891n.pdf

V.I. Ogievetsky

Papers

Theory of Dynamical Affine and Conformal Symmetries as Gravity Theory