Necessary and sufficient conditions for all order vanishing β-functions in supersymmetric Yang-Mills theories

All-loop Finite Unified Theories (FUTs) are very interesting N = 1 supersym- metric 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 dimension- ful 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.

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Finite Unification: Theory and Predictions ?

Finite Unified Theories (FUTs) are N = 1 supersymmetric Grand Unified Theories (GUTs) which can be made finite to all-loop orders, based on the principle of reduction of couplings, and therefore are provided with a large predictive power. Confronting the predictions of SU(5) FUTs with the top and bottom quark masses and other low-energy experimental constraints a light Higgs-boson mass in the range M_h \sim 121-126 GeV was predicted, in striking agreement with the recent discovery of a Higgs-like state around \sim 125.5 GeV at ATLAS and CMS. Furthermore the favoured model, a finiteness constrained version of the MSSM, naturally predicts a relatively heavy spectrum with coloured supersymmetric particles above \sim 1.5 TeV, consistent with the non-observation of those particles at the LHC. Restricting further the best FUT's parameter space according to the discovery of a Higgs-like state and B-physics observables we find predictions for the rest of the Higgs masses and the supersymmetric particle spectrum.

Finite Theories Before and After the Discovery of a Higgs Boson at the LHC

https://archive-ouverte.unige.ch/unige:119379/ATTACHMENT01

Adler-Bardeen theorem and vanishing of the gauge beta function☆

http://digital.csic.es/bitstream/10261/205476/4/reductiphysic.pdf

Reduction of couplings and its application in particle physics

The properties that make theN=4 super Yang-Mills theory free from ultraviolet divergences are (i) a universal coupling for gauge and matter interactions, (ii) anomaly-free representations, (iii) no charge renormalization, and (iv) if masses are explicitly introduced into the theory, then these are required to satisfy the mass-squared supertrace sum rule ∑s=0,1/2(−1)2s+1(2s+1)Ms2=0 FiniteN=2 theories are found to satisfy the above criteria The missing member in this class of field theories are finite field theories consisting ofN=1 superfields These theories are discussed in the light of the above finiteness properties In particular, the representations of all simple classical groups satisfying the anomaly-free and no-charge renormalization conditions for finiteN=1 field theories are discussed A consequence of these restrictions on the allowed representations is that anN=1 finiteSU (5)-based model of strong and electroweak interactions can contain at most five conventional families of quarks and leptons, a constraint almost compatible with the one deduced from cosmological arguments

J. G. Taylor

Papers

Toward finite quantum field theories