Revisiting Coupling Selection Rules in Heterotic Orbifold Models

TL;DR

This paper refines the understanding of coupling selection rules in heterotic orbifold models, introducing two additional rules that impact phenomenological aspects like proton decay and exotic mass matrices.

Contribution

It identifies and formalizes two new selection rules based on lattice symmetries and worldsheet instantons, enhancing the analysis of couplings in heterotic orbifold compactifications.

Findings

Refined selection rules affect coupling viability.

Many proton-decay operators are suppressed.

Exotic mass matrices remain unchanged.

Abstract

We study L-point couplings between twisted sector fields in heterotic orbifold compactifications, using conformal field theory. Selection rules provide an easy way to identify which couplings are non-vanishing. Those used in the current literature are gauge invariance, R-charge conservation and the space group selection rule, but they are not the whole story. We revive and refine a fourth selection rule, due to symmetries in the underlying torus lattice, and introduce a fifth one, due to the existence or not of classical worldsheet instanton solutions to mediate the couplings. We consider briefly the phenomenological consequences of the additional rules, in particular for recent orbifold constructions whose field content correspond to that of the MSSM. The structure of the exotic mass matrices is unaltered and many dimension-5 proton-decay operators vanish.