Revisiting coupling selection rules in heterotic orbifold models

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.

R-charge conservation and more in factorizable and non-factorizable orbifolds

“…Then we describe the basic ingredients of the corresponding worldsheet conformal field theory, in particular the vertex operators and correlation functions. Finally, we review how the correlation functions can be used to derive string coupling selection rules, referring to [13] for more details.…”

“…A first question one asks is which couplings in the action are allowed to be nonvanishing. The topic of selection rules for non-vanishing superpotential couplings in heterotic orbifold compactifications was revisited recently in [13]. By studying the corresponding L-point correlation functions, an apparently forgotten rule [14][15][16] was identified, and a new rule discovered.…”

Flavor structure in D-brane models: Majorana neutrino masses

“…1 Similar discrete flavor symmetries can be derived in heterotic string theory on orbifolds [23][24][25]. 2 In these models, we can calculate explicitly Yukawa couplings and higher order couplings [27][28][29][30][31][32][33][34][35][36][37][38][39].…”

Δ(54) flavor phenomenology and strings

“…Couplings among string states are subject to a set of constraints called string selection rules [86][87][88][89][90][91][92], due to symmetries of the underlying conformal field theory of the compactified string theory. These selection rules establish for which combination of string states there is a non-zero correlation function, and thus a non-zero coupling for the associated effective fields.…”