U-Duality and the Compactified Gauss-Bonnet Term
Journal article, 2007

We present the complete toroidal compactification of the Gauss-Bonnet Lagrangian from D dimensions to D-n dimensions. Our goal is to investigate the resulting action from the point of view of the "U-duality" symmetry SL(n+1,R) which is present in the tree-level Lagrangian when D-n=3. The analysis builds upon and extends the investigation of the paper [arXiv:0706.1183], by computing in detail the full structure of the compactified Gauss-Bonnet term, including the contribution from the dilaton exponents. We analyze these exponents using the representation theory of the Lie algebra sl(n+1,R) and determine which representation is the relevant one for quadratic curvature corrections. By interpreting the result of the compactification as a leading term in a large volume expansion of an SL(n+1,Z)-invariant action, we conclude that the overall exponential dilaton factor should not be included in the representation structure. As a consequence, all dilaton exponents correspond to weights of sl(n+1,R), which, nevertheless, remain on the positive side of the root lattice.


Ling Bao

Chalmers, Applied Physics, Mathematical Physics

Johan Bielecki

Chalmers, Applied Physics, Mathematical Physics

Martin Cederwall

Chalmers, Applied Physics, Mathematical Physics

Bengt E W Nilsson

Chalmers, Applied Physics, Mathematical Physics

Daniel Persson

Journal of High Energy Physics

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