Differential geometry with a projection: Application to double field theory

Details Differential geometry with a projection: Application to double field theory Differential geometry with a projection: Application to double field theory

2010-11-05

arxiv.org/abs/1011.1324v2

JHEP 1104:014,2011

Physics

High Energy Physics

High Energy Physics - Theory

1+22 pages, No figure; a previous result on 4-index tensor removed, presentation improved

Scientific paper

10.1007/JHEP04(2011)014

In recent development of double field theory, as for the description of the massless sector of closed strings, the spacetime dimension is formally doubled, i.e. from D to D+D, and the T-duality is realized manifestly as a global O(D,D) rotation. In this paper, we conceive a differential geometry characterized by a O(D,D) symmetric projection, as the underlying mathematical structure of double field theory. We introduce a differential operator compatible with the projection, which, contracted with the projection, can be covariantized and may replace the ordinary derivatives in the generalized Lie derivative that generates the gauge symmetry of double field theory. We construct various gauge covariant tensors which include a scalar and a tensor carrying two O(D,D) vector indices.

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