Superstring symmetries and space-time dimensionality

The value of the dimensionality of the physical space-time can be determined by the application of continuous and discrete symmetry principles to both the -dimensional effective action and the two-dimensional world-sheet action S (2) of the heterotic superstring theory. In particular, for a background Friedmann space-time generated by stringy matter with the equation of state , we show here that the world sheet is only supersymmetric, and only invariant under the time-reversal operator T, if . This is the condition that is invariant under T, and also for the realization of the non-linear global supersymmetry due to Volkov and Akulov.