Gauge couplings calculated from multiple point criticality yield alpha(-l)=137 +/- 9: At last, the elusive case of U(1)

We calculate the U(1) continuum gauge coupling using the values of action p arameters coinciding with the multiple point. This is a point in the phase diagram of a lattice gauge theory where a maximum number of phases convene. We obtain for the running inverse fine structure constant the values alpha (1)(-1) = 56 +/- 5 and alpha(1)(-1) = 99 +/- 5 at the Planck scale and the Mt scale, respectively. The gauge group underlying the phase diagram in whi ch we seek multiple point parameters is what we call the Anti-grand-unified theory (AGUT) gauge group SMG(3), which is the Cartesian product of three Standard Model Groups (SMG's). There is one SMG factor for each of the N-ge n = 3 generations of quarks and leptons. In our model, this gauge group SMG (3) is the predecessor of the usual SMG. The latter arises as the diagonal subgroup surviving the Planck scale breakdown of SMG(3). This breakdown lea ds to a weakening of the U(1) coupling by a N-gen-related factor. For N-gen = 3, this factor would be N-gen (N-gen + 1)/2 = 6 if phase transitions bet ween all the phases convening at the multiple point were purely second orde r. The factor N-gen (N-gen + 1)/2 = 6 corresponds to the six gauge-invarian t combinations of the N-gen = 3 different U(1)'s that give action contribut ions that are second order in F-mu nu. The factor analogous to this N-gen ( N-gen + 1)/2 = 6 in the case of the earlier considered non-Abelian coupling s reduced to the factor N-gen = 3 because action terms quadratic in F-mu nu that arise as contributions from two different of the N-gen = 3 SMG factor s of SMG(3) are forbidden by the requirement of gauge symmetry. Actually we seek the multiple point in the phase diagram of the gauge group U(1)3 as a simplifying approximation to the desired gauge group SMG(3). Th e most important correction obtained from using multiple point parameter va lues tin a multiparameter phase diagram instead of the single critical para meter value obtained, say, in the one-dimensional phase diagram of a Wilson action) comes from the effect of including the influence of also having at this point phases confined solely w.r.t. discrete subgroups. In particular , what matters is that the degree of first-orderness is taken into account in making the transition from these latter phases at the multiple point to the totally Coulomb-like phase. This gives rise to a discontinuity Delta ga mma(eff) in an effective parameter gamma(eff). Using our calculated value o f the quantity Delta gamma(eff), we calculate the above-mentioned weakening factor to be more like 6.5 instead of the N-gen (N-gen + 1)/2 = 6, as woul d be the case if all multiple point transitions were purely second order. U sing this same Delta gamma(eff), we also calculate the continuum U(1) coupl ing corresponding to the multiple point of a single U(1). The product of th is latter and the weakening factor of about 6.5 yields our Planck scale pre diction for the continuum U(1) gauge coupling, i.e. the multiple point crit ical coupling of the diagonal subgroup of U(1)(3) is an element of SMG(3). Combining this with the results of earlier work on the non-Abelian gauge co uplings leads to our prediction of alpha(-1) = 137 +/- 9 as the value for t he fine structure constant at low energies.