Self-duality and vacuum selection

TL;DR

This paper proposes that self-duality in quantum phase-space determines the selection of the quantum gravity vacuum, supported by string model phenomenology and a new formulation of quantum mechanics emphasizing phase-space duality.

Contribution

It introduces the idea that self-duality criteria in phase-space can select the quantum gravity vacuum, linking string models and quantum mechanics reformulation.

Findings

Free fermionic models are constructed near the self-dual point under T-duality.

Z2 x Z2 orbifolds fix moduli near the self-dual point.

Self-dual states correspond to critical points in duality-invariant systems.

Abstract

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 X Z2 toroidal orbifolds is discussed. Recent analysis revealed that the Z2 X 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.