Abstract
Phenomenologically appealing supersymmetric grand unified theories have large gauge representations and thus are not asymptotically free. Their ultraviolet validity is limited by the appearance of a Landau pole well before the Planck scale. One could hope that these theories save themselves, before the inclusion of gravity, by generating an interacting ultraviolet fixed point, similar to the one recently discovered in non-supersymmetric gauge-Yukawa theories. Employing a-maximization, a-theorem, unitarity bounds, as well as positivity of other central charges we nonperturbatively rule out this possibility for a broad class of prime candidates of phenomenologically relevant supersymmetric grand unified theories. We also uncover candidates passing these tests, which have either exotic matter or contain one field decoupled from the superpotential. The latter class of theories contains a model with the minimal matter content required by phenomenology.
Highlights
Appealing supersymmetric grand unified theories have large gauge representations and are not asymptotically free
Since the grand unified theories investigated here supersymmetric we have a number of consistency checks and general constraints at our disposal to analyse the potential existence of any RG fixed point. If such a RG fixed points exists in an N = 1 superconformal field theory (SCFT) it will necessarily possess a conserved U (1)R global symmetry
We mentioned in the introduction that non asymptotically free grand unifications can provide a rationale for the existence of low energy R parity [18,19,20]
Summary
Since the grand unified theories investigated here supersymmetric we have a number of consistency checks and general constraints at our disposal to analyse the potential existence of any RG fixed point. If such a RG fixed points exists in an N = 1 superconformal field theory (SCFT) it will necessarily possess a conserved U (1)R global symmetry. The U (1)R current is in the same supermultiplet [82] as the energy-momentum tensor and the supercharge currents; this leads to several exact relations and constraints that we briefly
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