Glasgow University, UK

*Larisa V. LAPERASHVILI*

Institute of Theor. and Exper. Physics, Moscow, RUSSIA

E-mail: laper@heron.itep.ru

*H.B. NIELSEN*

Niels Bohr Institute, Copenhagen, DENMARK

*Y. TAKANISHI*

ICTP, Trieste

**Family replicated gauge group models**

**Abstract:**

Recently it was shown by N.Arkani-Hamed, A.G.Cohen, H.Georgi et
al. that family replicated gauge groups (FRGG) of the type
SU(n)^{N}×SU(m)^{N} provide new directions for research in
high energy physics and quantum field theory. In their model of
Deconstruction of space-time, they tried to construct
renormalisable asymptotically free four dimensional gauge theories
which dynamically generate a fifth dimension (maybe more). Such
theories naturally lead to electroweak symmetry breaking, relying
neither on supersymmetry nor on strong dynamics at the TeV scale.
The new TeV physics is perturbative and radiative corrections to
the Higgs mass are finite. The new Higgs scalar is an extended
object - pseudo-Nambu-Goldstone boson
- and a novel Higgs potential emerges naturally requiring a
second light SU(2) doublet scalar. The extension of the Standard
Model (SM) with an FRGG-symmetry of the type G = (SMG)^{3} º [SU(3)_{c(color)}]^{3}×[SU(2)_{L(left)}]^{3}×[U(1)_{Y(hypercharge)}]^{3} was first suggested by D.L.Bennett,
H.B.Nielsen and I.Picek (1988) and developed by C.D.Froggatt and
H.B.Nielsen (*Origin of Symmetries*, 1991). This Anti-grand
unification theory (AGUT) assumes that at a scale ~ 10^{18}
GeV there is a spontaneous breakdown of the FRGG-symmetry to its
diagonal subgroup G_{diag}, which was identified with the usual
(low-energy) Standard Model group (SMG). The generalized gauge
group (SMG)^{3}×U(1)_{f(flavor)} was suggested by the
fitting of the SM fermion masses. But then H.B.Nielsen and
Y.Takanishi considered the further extended FRGG-symmetry
G_{ext} = (SMG×U(1)_{B-L})^{3} taking into account the
right-handed neutrinos. The FRGG G_{ext} was used by
C.D.Froggatt, H.B.Nielsen and Y.Takanishi to fit the SM fermion
masses and mixing angles and to describe all modern neutrino
experiments using only 5 free parameters - five VEVs of the
Higgs fields which break the FRGG-symmetry to the SM. This
typical fit is very encouraging. L.V.Laperashvili, H.B.Nielsen and
D.A.Ryzhikh have shown that the Abelian monopoles (existing also
in non-Abelian theories) in the FRGG-model have N^{*} times
smaller magnetic charge than in the SM, where N^{*} = N(N+1)/2.
These monopoles can appear at high energies in the FRGG-model and
give additional contributions to the beta-functions of the
renormalisation group equations for the running fine structure
constants a_{i}(m) (i=1,2,3 corresponds to the U(1), SU(2)
and SU(3) gauge groups of the SM). Taking into account these
monopole contributions, it was shown that, in contrast to the case
of AGUT, there exists the possibility of unifying all the gauge
couplings if the FRGG-breakdown occurs at the scale ~ 10^{14} GeV. In this talk we shall discuss all the above topics
and also briefly consider the possibility of [SU(5)]^{3} or
[SO(10)]^{3} unification at the GUT-scale ~ 10^{18} GeV.