# Safe Trinification

## TL;DR

This paper constructs a UV-safe Trinification model embedding the Standard Model, achieving an interacting fixed point and predicting a symmetry breaking scale around 10 TeV, with potential experimental implications.

## Contribution

It introduces a UV-safe Trinification theory with large flavor techniques, providing a UV completion of the Standard Model with specific phenomenological predictions.

## Key findings

- All couplings reach an interacting UV fixed point.
- The model matches the Standard Model in the IR.
- Symmetry breaking scale predicted around 10 TeV.

## Abstract

In this work, we provide a UV safe Trinification theory in which the Standard Model is embedded. Using recently developed large number-of-flavor techniques, safety is achieved by adding to the theory gauged vector-like fermions. We find that all gauge, scalar quartic, and Yukawa couplings achieve an interacting ultraviolet fixed point below the Planck scale. We find renormalization group flow solutions matching the Standard Model in the IR, indicating a truly UV completion of the Standard Model. Imposing constraints that realistic Higgs, top, bottom, tau and reasonable neutrino masses are recovered, we find the set of allowed solutions to be quite restrictive. Furthermore, the symmetry breaking scale is predicted to be around 10 TeV, making this model vulnerable to experiment.