U-Duality and the Compactified Gauss-Bonnet Term

Bao, Ling,1980Chalmers tekniska högskola,Chalmers University of Technology (författare)

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.

Bielecki, Johan,1982Chalmers tekniska högskola,Chalmers University of Technology(Swepub:cth)bieljoha (författare)
Cederwall, Martin,1961Chalmers tekniska högskola,Chalmers University of Technology(Swepub:cth)tfemc (författare)
Nilsson, Bengt E W,1952Chalmers tekniska högskola,Chalmers University of Technology(Swepub:cth)tfebn (författare)
Persson, Daniel (författare)
Chalmers tekniska högskola (creator_code:org_t)

Av författaren/redakt...: Bao, Ling, 1980; Bielecki, Johan, ...; Cederwall, Marti ...; Nilsson, Bengt E ...; Persson, Daniel

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