Aspects of higher curvature terms and U-duality

Abstract

We discuss various aspects of dimensional reduction of gravity with theEinstein-Hilbert action supplemented by a lowest order deformation formed asthe Riemann tensor raised to powers two, three or four. In the case of R^2 wegive an explicit expression, and discuss the possibility of extended cosetsymmetries, especially SL(n+1,Z) for reduction on an n-torus to threedimensions. Then we start an investigation of the dimensional reduction of R^3and R^4 by calculating some terms relevant for the coset formulation, aiming inparticular towards E_8(8)/(Spin(16)/Z_2) in three dimensions and aninvestigation of the derivative structure. We emphasise some issues concerningthe need for the introduction of non-scalar automorphic forms in order torealise certain expected enhanced symmetries.