Chiral rings and GSO projection in Orbifolds

TL;DR

This paper clarifies the GSO projection in orbifold string theories, providing a simple rule for chiral rings in various dimensions through partition function equivalence and mode analysis.

Contribution

It introduces a straightforward GSO projection rule for chiral rings in orbifold backgrounds, resolving previous ambiguities in the literature.

Findings

Unified GSO projection rule derived from partition function equivalence

Explicit mode analysis for constructing chiral rings

Clarification of subtleties in twisted sector GSO projections

Abstract

The GSO projection in the twisted sector of orbifold background is sometimes subtle and incompatible descriptions are found in literatures. Here, from the equivalence of partition functions in NSR and GS formalisms, we give a simple rule of GSO projection for the chiral rings of string theory in $\C^r/\Z_n$, $r=1,2,3$. Necessary constructions of chiral rings are given by explicit mode analysis.