Joint Theory Seminar: Holger Bech Nielsen

Title: Approximate SU(5) GUT, Fine Structure Constants

Abstract: We fit the three fine structure constants of the Standard Model with three, in first approximation theoretically
 estimable parameters,

1) a ``unified
 scale'',turning out not equal  to the Planck scale and thus
 only estimable by a very speculative story,

2) a ``number of layers'' being a priori the number of families, and

3) a unified coupling related to a critical coupling on a lattice.

So formally we postdict the three fine structure constants!

 In the philosophy of our model there is a physical lattice theory with link variables taking values in a (or in the various) ``small''
 representations of the Standard Model Group. We argue for that these representations function
 in first approximation as were the theory a genuine SU(5) theory. Next we
 take into account fluctuation of the gauge fields in the lattice and obtain a
 correction to the a priori SU(5) approximation, because of course the
 link fluctuations not corresponding any Standard model Lie algebra, but
 only to the SU(5), do not exist.

 The model is a development of our old anti-grand-unification model having as
 its genuine gauge group, close to fundamental scale, a cross product of the
 standard model group $S(U(3)\times U(2))$ with itself, there being  one
 Cartesian product factor for each family.

 In these old works we included the hypotesis of ``multiple point criticallity
 principle'' which here effectively means the coupling constants be critical
 on the lattice. Counted relative to the Higgs scale we suggest the in our
 sense ``unified scale'' (where the deviations between the inverse fine
 structure constants deviate by quantum fluctuations being only from
 standard model groups, not SU(5)) makes up the 2/3 th power of the Planck
 scale relative to the Higgs scale, or better the top quark mass scale.

Student session: 13:10