Asymptotically Safe Grand Unification

TL;DR

This paper investigates whether certain supersymmetric grand unified theories can be asymptotically safe via ultraviolet fixed points, and finds that most are ruled out, though some with exotic matter or decoupled fields remain viable.

Contribution

It nonperturbatively rules out asymptotic safety for a broad class of supersymmetric GUTs using advanced theoretical tools, identifying some candidate theories with special features.

Findings

Most supersymmetric GUTs are not asymptotically safe due to Landau poles.

Some theories with exotic matter or decoupled fields remain viable candidates.

A minimal matter content model consistent with phenomenology is identified.

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.