Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2003-05-30
Eur.Phys.J. C39 (2005) 483-497
Physics
High Energy Physics
High Energy Physics - Lattice
34 pages, 1 figure
Scientific paper
10.1140/epjc/s2004-02036-7
It has been proposed to abandon the requirement that parallel transporters in gauge theories are unitary (or pseudoorthogonal). This leads to a geometric interpretation of Vierbein fields as parts of gauge fields, and nonunitary parallel transport in extra directions yields Higgs fields. In such theories, the holonomy group H is larger than the gauge group G. Here we study a 1-dimensional model with fermions which retains only the extra dimension, and which is soluble in the sense that its renormalization group flow may be exactly computed, with G=SU(2) and noncompact subgroup H of GL(2,C), or G=U(2), H=GL(2,C). In all cases the asymptotic behavior of the Higgs potential is computed, and with one possible exception for G=SU(2), H=GL(2,C), there is a flow of the action from an UV-fix point which describes a SU(2)-gauge theory with unitary parallel transporters, to a IR-fixpoint. We explain how a splitting of the masses of fermions of different flavor can arise through spontaneous symmetry breaking.
Lehmann Claudia
Mack Gerhard
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