Fictitious Extra Dimensions
  String theory requires additional degrees of freedom to maintain world-sheet reparameterisation invariance at the quantum level. These are often interpreted as extra dimensions, beyond the 4 space-time. I discuss a class of quasi-realistic string models in which all the untwisted geometrical moduli are projected out by GSO projections. In these models the extra dimensions are fictitious, and do not correspond to physical dimensions in a low energy effective field theory. This raises the possibility that extra dimensions are fictitious in phenomenologically viable string vacua. I propose that self-duality in the gravitational quantum phase-space provides the criteria for the string vacuum selection. 
Alon E. Faraggi