Self–Duality and Vacuum Selection

I propose that self–duality in quantum phase–space provides the criteria for the selection of the quantum gravity vacuum. The evidence for this assertion arises from two independent considerations. The first is the phenomenological success of the free fermionic heterotic–string models, which are constructed in the vicinity of the self–dual point under T–duality. The relation between the free fermionic models and the underlying Z2×Z2 toroidal orbifolds is discussed. Recent analysis revealed that the Z2 × Z2 free fermionic orbifolds utilize an asymmetric shift in the reduction to three generations, which indicates that the untwisted geometrical moduli are fixed near the self–dual point. The second consideration arises from the recent formulation of quantum mechanics from an equivalence postulate and its relation to phase–space duality. In this context it is demonstrated that the trivial state, with V (q) = E = 0, is identified with the self–dual state under phase–space duality. These observations suggest a more general mathematical principle in operation. In physical systems that exhibit a duality structure, the self–dual states under the given duality transformations correspond to critical points. [email protected]