The importance of introducing the SO(5) singlet into the new novel model of non-Fermi liquid proposed by LeClair and collaborators is pointed out. This SO(5) singlet order parameter leads to a phase transition between the normal metal and the pseudog
ap region in the phase diagram for the anti-ferromagnetic (AF) phase and the (d-wave) superconducting (SC) phase. A non-zero value for this order can increase substantially the critical temperature of the SC transition.
In an earlier paper, it is proposed that, due to resonance tunneling effect, tunneling from a large cosmological constant $Lambda$ site in the stringy comic landscape can be fast, while tunneling from a small $Lambda$ site may take exponentially long
time. Borrowing the renormalization group analysis of the conductance in the Anderson localization transition, we treat the landscape as a multi-dimensional random potential and find that the vastness of the landscape leads to a sharp transition at a small critical value $Lambda_{c}$ from fast tunneling for $Lambda > Lambda_{c} $ to suppressed tunneling for $Lambda_{c} > Lambda >0$. Mobility in the landscape makes eternal inflation highly unlikely. As an illustration, we find that $Lambda_{c}$ can easily be exponentially small compared to the string/Planck scale. These properties may help us in finding a qualitative understanding why todays dark energy is so small.
