Self-Duality and Vacuum Selection

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 Z 2 ×Z 2 toroidal orbifolds is discussed. Recent analysis revealed that the Z 2 × Z 2 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. * faraggi@thphys.ox.ac.uk

Surveying the three-dimensional fixed points ofTduality

“…In Ref. [16] a Birkhoff's theorem was proven for the class of metrics (7) described by gravity in presence of a negative cosmological constant. In particular, it was proven that for a metric determined by the functions above there exists a coordinate system in which H 0 = 0.…”

“…Besides, the thermodynamics of the self-dual solutions presenting event horizons also exhibits particular properties [6], and it can be also thought of as an additional motivation to study it within the context of string theory in curved spacetime. More importantly, self-T-dual backgrounds are believed to play an important role in the search for string theory vacua [7].…”

Novel Perspectives in String Phenomenology

“…[14]. How this rich symmetry structure plays a role in the phenomenological properties of the models remains to be determined, and some novel suggestions have been articulated [15,16]. Among them the suggestion that self-duality under T -duality in string theory play a role in the vacuum selection [15], and the role of self-duality under spinor-vector duality [17] in light extra U (1) symmetries and light sterile neutrinos [16].…”

Novel Perspectives in String Phenomenology

“…[14]. How this rich symmetry structure plays a role in the phenomenological properties of the models remains to be determined, and some novel suggestions have been articulated [15,16]. Among them the suggestion that self-duality under T -duality in string theory play a role in the vacuum selection [15], and the role of self-duality under spinor-vector duality [17] in light extra U (1) symmetries and light sterile neutrinos [16].…”

“…How this rich symmetry structure plays a role in the phenomenological properties of the models remains to be determined, and some novel suggestions have been articulated [15,16]. Among them the suggestion that self-duality under T -duality in string theory play a role in the vacuum selection [15], and the role of self-duality under spinor-vector duality [17] in light extra U (1) symmetries and light sterile neutrinos [16]. Furthermore, the fact that the free fermionic models are constructed at an enhanced symmetry point in the toroidal moduli space, and the fact that the Z 2 × Z 2 orbifold can act on each of the six internal dimensions separately, enables the projection of all the internal geometrical moduli [10].…”