The cosmological constant problem in heterotic-M-theory and the orbifold of time

Abstract: Chameleon fields are quantum fields with an increasing mass as a function of the matter density of the environment. Recently chameleon fields have been exploited to solve the cosmological constant problem in the Modified Fujii's Model - MFM [Phys Rev D82 (2010) 044006]. However, gravity has been treated basically at a semiclassical level in that paper. In this article the stringy origin of the MFM is further discussed: as we will see, the MFM can be obtained from heterotic-M-theory. Consequently, a quantum description of gravity is obtained and the theory is finite because we choose the string mass as our UV cut-off. This stringy origin of the MFM creates stronger theoretical grounds for our solution to the cosmological constant problem. In our analysis, time will be compactified on a $S^1/Z_2$ orbifold and this peculiar compactification of time has a number of consequences. For example, as we will see, quantum gravity and a quantum gauge theory are actually the same theory in the sense that gravity is the time-evolution of a gauge theory. This might be the key to obtain a non-approximated stabilizing potential for the dilaton in the string frame. In this paper we will further discuss the non-equivalence of different conformal frames at the quantum level. As we will see, in our approach we use basically a unique conformal frame: the frame where the masses of particles are field dependent. A word of caution is necessary: we do not take into account massive string states and IR divergences.