Aspects of higher curvature terms and U-duality
arXiv:0706.1183 · doi:10.1088/0264-9381/25/9/095001
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.
26 pp., 15 figs., plain tex
References in corpus (30)
- E_11 and M Theory
- U-duality and M-Theory
- E10 and a "small tension expansion" of M Theory
- Dualisation of Dualities, I
- One loop in eleven dimensions
- Supersymmetry Constraints on Type IIB Supergravity
- Duality and higher derivative terms in M theory
- Symmetries of higher-order string gravity actions
- Supersymmetric higher-derivative actions in ten and eleven dimensions, the associated superalgebras and their formulation in superspace
- R^4, purified
- The Symmetry of M-Theories
- On Brillouin Zones
- Eisenstein Series and String Thresholds
- Sixteen-fermion and related terms in M-theory on T**2
- Manifestly supersymmetric M-theory
- Minimal representations, spherical vectors, and exceptional theta series I
- Higher order M theory corrections and the Kac-Moody algebra E10
- One-loop four-graviton amplitude in eleven-dimensional supergravity
- Supersymmetric Corrections to Eleven-Dimensional Supergravity
- Magnons, Classical Strings and beta-Deformations
- On Discrete U-duality in M-theory
- Higher Derivative Corrections to Eleven Dimensional Supergravity via Local Supersymmetry
- Symmetries,Singularities and the De-Emergence of Space
- Enhanced Coset Symmetries and Higher Derivative Corrections
- Curvature corrections and Kac-Moody compatibility conditions
- Duality Groups, Automorphic Forms and Higher Derivative Corrections
- R^4 Corrections to Eleven Dimensional Supergravity via Supersymmetry
- The octic E8 invariant
- U-duality covariant membranes
- Generalised 11-dimensional supergravity
Cited by in corpus (15)
- Automorphic properties of low energy string amplitudes in various dimensions
- Eisenstein series and automorphic representations
- Loops in exceptional field theory
- Duality Invariance and Higher Derivatives
- A master exceptional field theory
- Eisenstein series for infinite-dimensional U-duality groups
- Perturbation Theory From Automorphic Forms
- Constraints on Automorphic Forms of Higher Derivative Terms from Compactification
- U-Duality and the Compactified Gauss-Bonnet Term
- Automorphic Instanton Partition Functions on Calabi-Yau Threefolds
- Arithmetic and Hyperbolic Structures in String Theory
- Integral forms of Kac-Moody groups and Eisenstein series in low dimensional supergravity theories
- Fourier expansions of Kac-Moody Eisenstein series and degenerate Whittaker vectors
- Symmetries of non-maximal supergravities with higher-derivative corrections
- What U Can Do: New Solutions and New Challenges Beyond Leading Order