Four-dimensional “spacetime” from intersecting D-branes on the 9-torusT9

Abstract

A factorization of spacetime of the form M^3xM^3xM^3 is considered in this paper as the closed string background in type IIA. The idea behind this construction is that each M^3 might give rise to one large spatial dimension of 4-dimensional spacetime in the closed string sector. In the open string sector, intersecting D6-branes can be constructed for the simple choice of an orientifolded M^3=T^3 in a similar way as on the prominent T^6=T^2xT^2xT^2 using exact CFT. The D6-branes then are allowed to span general 2-cycles on each T^3. The intersection 1-cycles between two stacks of branes on one T^3 can be understood as one spatial dimension of the effective 4-dimensional 'spacetime' for the massless chiral fermions charged under these two stacks. Additionally to the known solutions to the R-R tadpole equations conserving (3+1)-dimensional Poincare invariance, this allows for solutions with globally just (2+1)- or (1+1)-Poincare invariance. For non-supersymmetric solutions, a string tree-level and one-loop potential for the scalar moduli (including the spacetime radii) is generated in the NS-NS sector. This potential here is interpreted dynamically for radii and dilaton in order to describe the global evolution of the universe. In the late time picture, (3+1)-dimensional global Poincare invariance can be restored well within experimental bounds. This approach links particle properties (the massless chiral fermion spectrum) directly to the global evolution of the universe by the scalar potential, both depending on the same topological wrapping numbers. In the future, this might lead to much better falsifiable phenomenological models.