E11, Brane Dynamics and Duality Symmetries

Following hep-th/0412336 we use the non-linear realisation of the semi-direct product of E11 and its vector representation to construct brane dynamics. The brane moves through a spacetime which arises in the non-linear realisation from the vector representation and it contains the usual embedding coordinates as well as the world volume fields. The resulting equations of motion are first order in derivatives and can be thought of as duality relations. Each brane carries the full E11 symmetry and so the Cremmer-Julia duality symmetries. We apply this theory to find the dynamics of the IIA and IIB strings, the M2 and M5 branes, the IIB D3 brane as well as the one and two branes in seven dimensions.Comment: 41 page

A sketch of brane dynamics in seven and eight dimension using E theory

Using the general properties that have emerged from E theory we sketch the generic features of the dynamics of branes in seven and eight dimensions. The dynamical equations are a set of duality equations involving the coordinates of the vector representation of E11.Comment: 17 page

E11, generalised space-time and IIA string theory

As advocated in hep-th/0307098 we construct the non-linear realisation of the semi-direct product of E11 and its first fundamental representation at lowest level from the IIA viewpoint. We find a theory that is SO(10,10)x GL(1) invariant and contains the fields of gravity, a two form and a dilaton but which depend on coordinates which belong to the vector representation of SO(10,10). The resulting Lagrangian agrees that of recent work on the so called doubled field theory. However, the construction given in this paper is straightforward and systematic. It also reveals the relevant underlying symmetries and opens the way to include the Ramond-Ramond, and higher level, fields together with additional coordinates of the generalised space-time.Comment: 15 page

Brane dynamics, central charges and E_{11}

We consider a theory in which supersymmetry is partially spontaneously broken and show that the dynamical fields in the same supersymmetric multiplet as the Goldstino are Goldstone bosons whose corresponding generators are central charges in the underlying supersymmetry algebra. We illustrate how this works for four dimensional Born-Infeld theory and five brane of M theory. We conjecture, with supporting arguments, that the dynamics of the branes of M theory can be extended so as to possess an E_{11} symmetry.Comment: 19 pages, plain te

E theory in seven dimensions

We construct the non-linear realisation of the semi-direct product of E11 and its vector representation in its decomposition into the subalgebra GL(7)x SL(5) to find a seven dimensional theory. The resulting equations of motion essentially follow from the Dynkin diagram of E11 and if one restricts them to contain only the usual fields of supergravity and the derivatives with respect to the usual coordinates of spacetime then these are the equations of motion of seven dimensional supergravity.Comment: 36 page

Poisson equations, higher derivative automorphic forms and string parameter limits

This paper considers the higher derivative terms in the effective action of type II string theory and in particular the behaviour of the automorphic forms they contain in all the different possible limits of the string parameters. The automorphic forms are thought to obey Poisson equations which contain the Laplacian defined on the coset space to which the scalars fields belong and we compute this Laplacian in all the possible string theory limits. We also consider these Poisson equations in the decompactification limit of a single dimension and by making two assumptions, one on the generic form of this equation and the other on the behaviour of the automorphic forms in this limit, we find strong constraints on the allowed form of this differential equation. We show that these constraints allow one to recover much of what was previously known about the automorphic forms corresponding to terms in the effective action that have fourteen or fewer space-time derivatives in a simple way.Comment: 47 pages, references added and typos correcte