# No-Scale SU(5) Super-GUTs

## TL;DR

This paper explores no-scale super-GUT models based on minimal SU(5), addressing proton decay, dark matter, and Higgs mass constraints, and identifies conditions for consistent solutions with potential dark matter detection.

## Contribution

It demonstrates that consistent no-scale super-GUT SU(5) models require at least one GUT Higgs fiveplet in a twisted chiral supermultiplet with specific modular weights.

## Key findings

- Consistent solutions exist with at least one GUT Higgs fiveplet in a twisted chiral supermultiplet.
- Some solutions predict detectable spin-independent dark matter scattering.
- Models without twisted chiral assignments are inconsistent.

## Abstract

We reconsider the minimal SU(5) Grand Unified Theory (GUT) in the context of no-scale supergravity, assuming that the soft supersymmetry-breaking parameters satisfy universality conditions at some input scale M_in above the GUT scale M_GUT. When setting up such a no-scale super-GUT model, special attention must be paid to avoiding the Scylla of rapid proton decay and the Charybdis of an excessive density of cold dark matter, while also having an acceptable mass for the Higgs boson. We do not find consistent solutions if none of the matter and Higgs fields are assigned to twisted chiral supermultiplets, even in the presence of Giudice-Masiero terms. However, consistent solutions may be found if at least one fiveplet of GUT Higgs fields is assigned to a twisted chiral supermultiplet, with a suitable choice of modular weights. Spin-independent dark matter scattering may be detectable in some of these consistent solutions.