Comments on Flipped SU(5) (and F-theory)

TL;DR

This paper analyzes the effects of nonrenormalizable operators in flipped SU(5), exploring their implications for F-theory model building, and proposes alternative approaches to GUT-Higgs engineering.

Contribution

It characterizes symmetries controlling dangerous operators in flipped SU(5) and discusses their realization in F-theory, proposing an alternative SU(5)  U(1)_{\u03c7} construction.

Findings

Nonrenormalizable operators can induce large  terms, R-parity violation, and proton decay.

Controlling symmetries are identified that can suppress unwanted operators.

A sample SU(5)  U(1)_{\u03c7} construction is presented as an alternative model.

Abstract

We study the impact of nonrenormalizable operators in flipped SU(5) that can generate a large mu term, R-parity violation, and rapid proton decay. While our motivation is to determine whether F-theory can naturally realize flipped SU(5), this analysis is general and leads to a characterization of symmetries capable of controlling such operators and should be independent of F-theory. We then discuss some specific implications for F-theory model building, where a significant mu problem is unavoidable. Finally, we mention previously noted difficulties associated to engineering GUT-Higgs fields in F-theory, suggest a direct engineering of SU(5) \times U(1)_{\chi} as an alternative, and present a sample construction of this type.