Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 6 (2010), 049, 29 pages      arXiv:1001.0428      https://doi.org/10.3842/SIGMA.2010.049
Contribution to the Proceedings of the Eighth International Conference Symmetry in Nonlinear Mathematical Physics

Finite Unification: Theory and Predictions

Sven Heinemeyer a, Myriam Mondragón b and George Zoupanos c, d
a) Instituto de Física de Cantabria (CSIC-UC), Santander, Spain
b) Instituto de Física, Universidad Nacional Autónoma de México, Apdo. Postal 20-364, México 01000, México
c) Theory Group, Physics Department, CERN, Geneva, Switzerland
d) Physics Department, National Technical University, 157 80 Zografou, Athens, Greece

Received January 03, 2010, in final form May 25, 2010; Published online June 11, 2010

Abstract
All-loop Finite Unified Theories (FUTs) are very interesting N=1 supersymmetric Grand Unified Theories (GUTs) which not only realise an old field theoretic dream but also have a remarkable predictive power due to the required reduction of couplings. The reduction of the dimensionless couplings in N=1 GUTs is achieved by searching for renormalization group invariant (RGI) relations among them holding beyond the unification scale. Finiteness results from the fact that there exist RGI relations among dimensionless couplings that guarantee the vanishing of all beta-functions in certain N=1 GUTs even to all orders. Furthermore developments in the soft supersymmetry breaking sector of N=1 GUTs and FUTs lead to exact RGI relations, i.e. reduction of couplings, in this dimensionful sector of the theory too. Based on the above theoretical framework phenomenologically consistent FUTS have been constructed. Here we present FUT models based on the SU(5) and SU(3)3 gauge groups and their predictions. Of particular interest is the Higgs mass prediction of one of the models which is expected to be tested at the LHC.

Key words: unification; gauge theories; finiteness; reduction of couplings.

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