Coset Symmetries Research Articles

Aspects of higher curvature terms and U-duality

We discuss various aspects of the dimensional reduction of gravity with the Einstein–Hilbert action supplemented by a lowest-order deformation formed as the Riemann tensor raised to powers two, three or four. In the case of R2 we give an explicit expression, and discuss the possibility of extended coset symmetries, especially for reduction on an n-torus to three dimensions. Then we start an investigation of the dimensional reduction of R3 and R4 by calculating some terms relevant for the coset formulation, aiming in particular towards in three dimensions and an investigation of the derivative structure. We emphasize some issues concerning the need for the introduction of non-scalar automorphic forms in order to realize certain expected enhanced symmetries.

Enhanced coset symmetries and higher derivative corrections

After dimensional reduction to three dimensions, the lowest order effective actions for pure gravity, M theory, and the bosonic string admit an enhanced symmetry group. In this paper we initiate study of how this enhancement is affected by the inclusion of higher derivative terms. In particular we show that the coefficients of the scalar fields associated to the Cartan subalgebra are given by weights of the enhanced symmetry group.

Coset symmetries in dimensionally reduced heterotic supergravity

We investigate the coset structures which appear in the dimensional reduction of supergravity theories. Especially we investigate how to recognize the global symmetry groups if the coset is non-split. As an example we apply our analysis to the theories emanating from the dimensional reduction of Heterotic supergravity.

Diagrammar and metamorphosis of coset symmetries in dimensionally reduced type IIB supergravity

Studying the reduction of type IIB supergravity from ten to three space-time dimensions we describe the metamorphosis of Dynkin diagram for gravity line "caterpillar" into a type IIB supergravity "dragonfly" that is triggered by inclusion of scalars and antisymmetric tensor fields. The final diagram corresponds to type IIB string theory E8 global symmetry group which is the subgroup of the conjectured E11 hidden symmetry group. Application of the results for getting the type IIA/IIB T-duality rules and for searching for type IIB vacua solutions is considered.

Coset symmetries in dimensionally reduced bosonic string theory

We discuss the dimensional reduction of various effective actions, particularly that of the closed bosonic string and pure gravity, to two and three dimensions. The result for the closed bosonic string leads to coset symmetries which are in agreement with those recently predicted and argued to be present in a new unreduced formulation of this theory. We also show that part of the Geroch group appears in the unreduced duality symmetric formulation of gravity recently proposed. We conjecture that this formulation can be extended to a non-linear realisation based on a Kac–Moody algebra which we identify. We also briefly discuss the proposed action of bosonic M-theory.