Aspects of higher curvature terms and U-duality

TL;DR

This paper explores the effects of higher curvature terms in gravity, their dimensional reduction, and the potential for extended symmetries like U-duality, with a focus on R^2, R^3, and R^4 deformations and their implications for coset structures.

Contribution

It provides explicit expressions for R^2 terms, investigates the reduction of R^3 and R^4, and discusses the role of automorphic forms in realizing enhanced symmetries.

Findings

Explicit R^2 expression derived.

Analysis of coset symmetries in reduced theories.

Highlighting the necessity of automorphic forms for symmetry realization.

Abstract

We discuss various aspects of 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 R^2 we give an explicit expression, and discuss the possibility of extended coset symmetries, especially SL(n+1,Z) for reduction on an n-torus to three dimensions. Then we start an investigation of the dimensional reduction of R^3 and R^4 by calculating some terms relevant for the coset formulation, aiming in particular towards E_8(8)/(Spin(16)/Z_2) in three dimensions and an investigation of the derivative structure. We emphasise some issues concerning the need for the introduction of non-scalar automorphic forms in order to realise certain expected enhanced symmetries.