R-charge Conservation and More in Factorizable and Non-Factorizable Orbifolds

TL;DR

This paper investigates the origin of R-charge conservation in heterotic orbifold compactifications, revealing new contributions and selection rules that refine our understanding of string coupling constraints in various orbifold types.

Contribution

It introduces a previously overlooked contribution to R-charge conservation from Gamma-phases and proposes a new string selection rule called Rule 6.

Findings

Gamma-phase contributions weaken R-charge selection rules

Symmetries among worldsheet instantons lead to additional selection rules

Identification of a new Rule 6 or 'coset vector selection rule'

Abstract

We consider the string theory origin of R-charge conservation laws in heterotic orbifold compactifications, deriving the corresponding string coupling selection rule for factorizable and non-factorizable orbifolds, with prime ordered and non-prime ordered point groups. R-charge conservation arises due to symmetries among the worldsheet instantons that can mediate the couplings. Among our results is a previously missed non-trivial contribution to the conserved R-charges from the Gamma-phases in non-prime orbifolds, which weakens the R-charge selection rule. Symmetries among the worldsheet instantons can also lead to additional selection rules for some couplings. We make a similar analysis for Rule 4 or the 'torus lattice selection rule'. Moreover, we identify a new string selection rule, that we call Rule 6 or the 'coset vector selection rule'.