weakness of gravity on distances> ∼ 1 mm is due to the existence of n ≥ 2 new compact spatial dimensions large compared to the weak scale. The Planck scale MPl ∼ G −1/2 N is not a fundamental scale; its enormity is simply a consequence of the large size of the new dimensions. While gravitons can freely

is fundamentally higher dimensional with 4+n spacetime dimensions, then the effective four-dimensional (reduced) Planck scale, MPl = 2 ×10 18 GeV, is determined by the fundamental (4+n)-dimensional Planck scale, M, and the geometry of the extra dimensions.

of interacting QFT and of the smoothing of ultraviolet divergences is deferred to a subsequent paper. In the classical limit where the Planck length goes to zero, our Quantum Spacetime reduces to the ordinary Minkowski space times a two component space whose components are homeomorphic to the tangent bundle TS 2

by the Planck scale, MPl [1]. It is also often sloppily said that R-parity prohibits proton decay in SUSY theories. Though R-parity prohibits the renormalizable B- and L-violating operators, it still allows the nonrenormalizable superpotential terms 1 M QQQL and 1 M UUDE, which contain dimension five operators

We describe briefly new program for SUSY masses calculations. The main distinction of our program is that we start to solve the renormalization group equations for soft SUSY breaking parameters for SU(5) SUSY GUT model from Planck scale MPL = 2.4 · 10 18 Gev. Our program works also for large tan

We argue that the familiar gauge hierarchy between the fundamental Planck scale MPl and the electroweak scale MW, can be naturally explained in higher dimensional theories with relatively large radii (Rc> 1/MPl) extra dimensions. In particular, we show that it is possible that the electroweak

-level unitarity is already violated at energies ∼ √ mMPl, rather than at the Planck scale MPl, even for m ≪ MPl. We then restore unitarity to this amplitude up to MPl by adding non-minimal couplings that depend on the curvature and its derivatives, and modify the minimal description – including particle

scenario of moduli stabilization, which is endowed with a hierarchy between the mass of the lightest modulus, the gravitino mass and the scale of the soft terms, mmodulus ∼ 〈X〉m 3/2 ∼ 〈X 〉 2 msoft. The ‘little hierarchy ’ 〈X 〉 is given by the logarithm of the ratio of the Planck scale and the gravitino

of the volume diagonalize also the area operator. We argue that the spectra of volume and area determined here can be considered as predictions of the loop-representation formulation of quantum gravity on the outcomes of (hypothetical) Planck-scale sensitive measurements of the geometry of space.

It is sometimes argued that a virtue of pushing the supersymmetry breaking scale above 1 PeV is that no particular flavor structure is required in the soft sector in order to evade bounds on flavor-changing neutral currents. However, without flavor structure, suppressing generic Planck