SU(5) orientifolds, Yukawa couplings, Stringy Instantons and Proton Decay

TL;DR

The paper constructs and analyzes SU(5) and flipped SU(5) orientifold vacua using Gepner-model RCFT methods, focusing on perturbative Yukawa absence and the generation of missing Yukawas through D-instantons. It classifies quartic and lower-order superpotential terms by their baryon/lepton-number violating potential and studies the zero-mode structure of instantons to determine which terms can be generated non-perturbatively. A key finding is that instanton effects generally produce both required Yukawas and dangerous proton-decay operators, necessitating either symmetry protections (e.g., a $Z_2$ R-symmetry) or significant tuning. The authors perform an extensive search for suitable instanton branes, identifying a small set of vacua where the desired Yukawas are generated without introducing unacceptable operators, and discuss the phenomenological implications for proton decay in these string-derived GUT frameworks.

Abstract

We construct a large class of SU(5) orientifold vacua with tadpole cancellation both for the standard and the flipped case. We give a general analysis of superpotential couplings up to quartic order in orientifold vacua and identify the properties of needed Yukawa couplings as well as the baryon number violating couplings. We point out that successful generation of the perturbatively forbidden Yukawa couplings entails a generically disastrous rate for proton decay from an associated quartic term in the superpotential, generated from the same instanton effects. We search for the appropriate instanton effects that generate the missing Yukawa couplings in the SU(5) vacua we constructed and find them in a small subset of them.