Issue Eur. Phys. J. C Volume 39, Number 4, February 2005 Page(s) 483 - 497 DOI 10.1140/epjc/s2004-02036-7

Eur. Phys. J. C 39, 483-497 (2005)
DOI: 10.1140/epjc/s2004-02036-7

Gauge theories with non-unitary parallel transporters: a soluble Higgs model^*

C. Lehmann and G. Mack

II. Institut für Theoretische Physik, Universität Hamburg, Hamburg, Germany

gerhard.mack@desy.de

(Received: 2 June 2003, Revised: 14 September 2004, Published online: 21 January 2005)

Abstract

It has been proposed to abandon the requirement that parallel transporters in gauge theories are unitary (or pseudo-orthogonal). This leads to a geometric interpretation of Vierbein fields as parts of gauge fields, and non-unitary 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 one-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 non-compact , 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 a UV fixed point which describes a SU(2)-gauge theory with unitary parallel transporters, to a IR fixed point. We explain how exponential mass ratios of fermions of different flavor can arise through spontaneous symmetry breaking, within the general framework.

PACS
11.10.Hi
11.10.Kk
11.15.Ex
11.15.Tk
12.15.Ff
12.15.Hh

Correspondence: gerhard.mack@desy.de


© Società Italiana di Fisica, Springer-Verlag 2005

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