English

Grand Pleromal Transmutation : condensates via Konsishi anomaly, dimensional transmutation and ultraminimal GUTs

High Energy Physics - Phenomenology 2020-08-18 v4

Abstract

Using consistency requirements relating chiral condensates imposed by the so called Generalized Konishi Anomaly, we show that dimensional transmutation via gaugino condensation {\emph{in the ultraviolet}} drives gauge symmetry breaking in a large class of {\emph{asymptotically strong}} Super Yang Mills Higgs theories. For Adjoint multiplet type chiral superfields Φ\Phi (transforming as r×rˉr \times \bar 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 ΛUVMXe8π2g2(MX)b0\Lambda_{UV} \simeq M_X \, e^{\frac{8\pi^2}{ g^2(M_X) b_0}} which determines the gaugino condensate. Thus the gauge coupling at the perturbative unification scale MXM_X 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),Qˉ(rˉ))({\bf Q}(r),{ \bf\bar Q}(\bar r)) or (\Sig((rr)symm)),\Sigb((rˉrˉ)symm) (\Sig((r\otimes r)_{symm})), \Sigb(({\bar r \otimes\bar r})_{symm}), that form trilinear matrix gauge invariants QˉΦQ,\SigbΦ\Sig\bar Q\cdot \Phi\cdot Q, \Sigb \cdot \Phi\cdot \Sig with Φ\Phi. Novel, robust and {\emph{ultraminimal}} Grand unification algorithms emerge from the analysis. We sketch the structure of a realistic Spin(10) model, with the 1616-plet of Spin(10) as the base representation rr, 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.

Keywords

Cite

@article{arxiv.2001.05803,
  title  = {Grand Pleromal Transmutation : condensates via Konsishi anomaly, dimensional transmutation and ultraminimal GUTs},
  author = {Charanjit S. Aulakh},
  journal= {arXiv preprint arXiv:2001.05803},
  year   = {2020}
}

Comments

Published version. Section 2.2 (added in v2,v3 to educate reluctant referee) has been removed as redundant because judged obviously known to any competent reader by accepting referee ! Thus v4 is very close to v1 except for correction of a significant typo in eqn(34) section 4.1