The Potential Fate of Local Model Building

TL;DR

This work analyzes local $E_8$-point models in F-theory GUTs to assess their ability to yield proton-stable interactions and realistic Yukawa textures. By constructing two candidate local models distinguished by matter parity (Case I and Case II), it tests their viability and finds that neither can be embedded in a globally consistent semilocal framework via spectral cover methods. The semilocal analysis imposes flux and chirality constraints that render both models inconsistent, signaling that global (nonlocal) ingredients are essential for realistic string-model building. The results suggest that predictions from purely local constructions should be treated with caution and motivate exploring beyond spectral-cover approaches to achieve fully consistent string vacua.

Abstract

We analyse local models at the point of E_8 in F-theory GUTs and identify exactly two models with potentially realistic properties concerning proton stability and a suitable pattern of quark and lepton masses. To this end we identify a matter parity at the local point. A globally consistent ultraviolet completion turns out to be problematic for both models. It is impossible to embed the models in a semilocal scheme via the spectral cover approach. This seems to severely limit the predictive power of local model building and to indicate that the full string theory might give us valuable hints for particle physics model building.