Differential geometry with a projection: Application to double field theory
arXiv:1011.1324 · doi:10.1007/JHEP04(2011)014
Abstract
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.
1+22 pages, No figure; a previous result on 4-index tensor removed, presentation improved
References in corpus (9)
- Double Field Theory
- The gauge algebra of double field theory and Courant brackets
- Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
- A field-theory motivated approach to symbolic computer algebra
- T-duality and closed string non-commutative (doubled) geometry
- Background Field Equations for the Duality Symmetric String
- Duality Symmetric Strings, Dilatons and O(d,d) Effective Actions
- E11, generalised space-time and IIA string theory
- Real fermionic symmetry in type II supergravity