In a recent paper it was shown that fundamental strings are null waves in Double Field Theory. Similarly, membranes are waves in exceptional extended geometry. Here the story is continued by showing how various branes are Kaluza-Klein monopoles of these higher dimensional theories. Examining the specific case of the E 7 exceptional extended geometry, we see that all branes are both waves and monopoles. Along the way we discuss the O(d, d) transformation of localized brane solutions not associated to an isometry and how true T-duality emerges in Double Field Theory when the background possesses isometries.

We construct the 12-dimensional exceptional field theory associated to the group SL(2)× R + . Demanding the closure of the algebra of local symmetries leads to a constraint, known as the section condition, that must be imposed on all fields. This constraint has two inequivalent solutions, one giving rise to 11-dimensional supergravity and the other leading to F-theory. Thus SL(2) × R + exceptional field theory contains both F-theory and M-theory in a single 12-dimensional formalism.

We formulate a kinematical extension of Double Field Theory on a 2d-dimensional para-Hermitian manifold (P, η, ω) where the O(d, d) metric η is supplemented by an almost symplectic two-form ω. Together η and ω define an almost bi-Lagrangian structure K which provides a splitting of the tangent bundle T P = L ⊕L into two Lagrangian subspaces. In this paper a canonical connection and a corresponding generalised Lie derivative for the Leibniz algebroid on T P are constructed. We find integrability conditions under which the symmetry algebra closes for general η and ω, even if they are not flat and constant. This formalism thus provides a generalisation of the kinematical structure of Double Field Theory. We also show that this formalism allows one to reconcile and unify Double Field Theory with Generalised Geometry which is thoroughly discussed.

Abstract:We examine the equations of motion of double field theory and the duality manifest form of M-theory. We show the solutions of the equations of motion corresponding to null waves correspond to strings or membranes from the usual spacetime perspective. A Goldstone mode analysis of the null wave solution in double field theory produces the equations of motion of the duality manifest string.

It has been known for a while that the effective geometrical description of compactified strings on d-dimensional target spaces implies a generalization of geometry with a doubling of the sets of tangent space directions. This generalized geometry involves an O(d, d) pairing η and an O(2d) generalized metric H. More recently it has been shown that in order to include T-duality as an effective symmetry, the generalized geometry also needs to carry a phase space structure or more generally a para-Hermitian structure encoded into a skew-symmetric pairing ω. The consistency of string dynamics requires this geometry to satisfy a set of compatibility relations that form what we call a Born geometry. In this work we prove an analogue of the fundamental theorem of Riemannian geometry for Born geometry. We show that there exists a unique connection which preserves the Born structure (η, ω, H) and which is torsionless in a generalized sense. This resolves a fundamental ambiguity that is present in the double field theory formulation of effective string dynamics.