Abstract
Using consistency requirements relating chiral condensates imposed by the so called Generalized Konishi Anomaly, we show that dimensional transmutation via gaugino condensation in the ultraviolet drives gauge symmetry breaking in a large class of asymptotically strong Super Yang Mills Higgs theories. For Adjoint multiplet type chiral superfields Φ (transforming as r×r¯ representations of a non Abelian gauge group G), solution of the Generalized Konishi Anomaly (GKA) equations allows calculation of quantum corrected VEVs in terms of the dimensional transmutation scale ΛUV≃MXe8π2g2(MX)b0 which determines the gaugino condensate. Thus the gauge coupling at the perturbative unification scale MX generates GUT symmetry breaking VEVs by non-perturbative dimensional transmutation. This obviates the need for large (or any) input mass scales in the superpotential. Rank reduction can be achieved by including pairs of chiral superfields transforming as either (Q(r),Q¯(r¯)) or (Σ((r⊗r)symm)),Σ‾((r¯⊗r¯)symm), that form trilinear matrix gauge invariants Q¯⋅Φ⋅Q,Σ‾⋅Φ⋅Σ with Φ. Novel, robust and ultraminimal Grand unification algorithms emerge from the analysis. We sketch the structure of a realistic Spin(10) model, with the 16-plet of Spin(10) as the base representation r, which mimics the realistic Minimal Supersymmetric GUT but contains even fewer free parameters. We argue that our results point to a large extension of the dominant and normative paradigms of Asymptotic Freedom/IR colour confinement and potential driven spontaneous symmetry breaking that have long ruled gauge theories.
Highlights
It has been a longstanding dream [1] to provide a mechanism for dynamical generation of the Grand Unification scale from the low energy (i.e. Electro-weak) data
In this paper we argue that Generalized Konishi anomaly (GKA) techniques allow fully quantum and non-perturbative calculation of chiral VEVs in terms of assumed underlying gaugino condensates in our [4,5] asymptotically strong(AS) dynamical symmetry breaking scenario
Using Generalized Konishi Anomaly relations obeyed by gluino and scalar condensates in supersymmetric vacua we have shown that asymptotically strong Supersymmetric Yang Mills Higgs theories with matrix type Higgs multiplets transforming as general matrix type base r tensors of G provide a calculable implementation of spontaneous symmetry breaking of the gauge group, including rank reduction, via dimensional transmutation
Summary
It has been a longstanding dream [1] to provide a mechanism for dynamical generation of the Grand Unification scale from the low energy (i.e. Electro-weak) data. In analogy with the behaviour at strong coupling in the AF case one expects that a supersymmetric Sigma model involving these gauge singlet but ’t Hooft anomaly matched ‘chiral moduli’ fields describes the UV phase [5] Be that as it may, the symmetry restored, UV phase expected on general grounds such as RG flows is not the subject of the investigations in this paper beyond the fact that, again in direct analogy with SuSy QCD, we expect gauge invariant, physical, chiral condensates to form in this phase. We emphasise that the parameters describing (a few) irreducible gauge singlet physical condensates are to be deduced in principle from the non-perturbative dynamics of the UV symmetry restored phase using, say, Lattice methods They are unknown dimensionful input parameters playing a VEV determining role similar to the mass parameters of standard SuSy GUT superpotentials. In Section 6. we discuss our results and the outlook for further work from a general view point
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