Could Fermion Masses Play a Role in the Stabilization of the Dilaton in Cosmology?

TL;DR

This paper investigates whether fermion masses can generate an effective potential that stabilizes the Dilaton in cosmology, considering quantum corrections and various mass generation mechanisms.

Contribution

It introduces a model where fermion masses contribute to the Dilaton potential, showing that quantum effects can create a stabilizing minimum.

Findings

Fermion mass contributions can produce a potential minimum for the Dilaton.

Quantum two-loop calculations support the stabilization mechanism.

The model applies to various fermion mass generation scenarios.

Abstract

We study the possibility that the Dilaton is stabilized by the contribution of fermion masses to its effective potential. We consider the Dilaton gravity action in four dimensions to which we add a mass term for a Dirac fermion. Such an action describes the interaction of the Dilaton with the fermions in the Yang-Mills sector of the coupled supergravity/super-Yang-Mills action which emerges as the low energy effective action of superstring theory after the extra spatial dimensions have been fixed. The Dilaton couples to the Fermion mass term via the usual exponential factor of this field which multiplies the non-kinetic terms of the matter Lagrangian, if we work in the Einstein frame. In the kinetic part of the Fermion action in the Einstein frame the Dilaton does not enter. Such masses can be generated in several ways: they can arise as a consequence of flux about internal spatial dimensions, they may arise as thermal fermion masses in a quasi-static phase in the early universe, and they will arise after the breaking of supersymmetry at late times. The vacuum contribution to the potential for the Dilaton is evaluated up to two loops. The result shows a minimum which could stabilize the Dilaton for reasonable ranges of parameter values.