Multiple Point Criticality, Nonlocality, and Finetuning in fundamental   physics: predictions for Gauge Coupling Constants gives   $\alpha^{-1}=136._8\pm 9
  The Multiple Point Criticality Principle (MPCP) states that action parameters - in for example a field theory - take on values corresponding to the junction of a maximum number of phases in the phase diagram of a system that undergoes phase transitions. The phases to which physical significance is ascribed are normally regarded as artifacts of a regulation procedure. In the context of a Y-M lattice gauge theory, the MPCP is applied to the system of different (Planck scale) lattice phases that can be provoked using a suitably generalised action with a gauge group that is taken to be the Planck scale predecessor to the Standard Model Group (SMG) - namely the $N_{gen}$-fold Cartesian product of the SMG. Here $N_{gen}$ is the number of fermion generations. Ambiguities under mappings of the gauge group $SGM^{N_{gen}}$ onto itself result in the Planck scale breakdown to the diagonal subgroup which is isomorphic to the usual SMG. Assuming the validity of the MPCP, the three SMG gauge couplings at the Planck scale are predicted to be equal to the diagonal subgroup couplings correspond- ing to the multiple point action parameters in a lattice gauge theory with the gauge group $SMG^{N_{gen}}$. This prediction gives agreement with experiment to within 10 \% for the non-Abelian couplings and 5\% for the U(1) gauge coup- ling. In a more general context, the MPCP is proposed as a fundamental princi- ple of Nature that can also explain other fine-tuning enigma in high energy physics. It is argued that the MPCP implies having long range nonlocal inter- actions which are identical between fields at all pairs of spacetime points. Such interactions are allowed in a very general form of a reparameterization invariant action. This phenomenologically unobjectionable form of nonlocality would quite naturally be incorporated into our theory as constants of Nature. 
Donald L. Bennett (The Niels Bohr Institute)