On the Construction of Asymmetric Orbifold Models

TL;DR

This paper investigates the construction of asymmetric orbifold models, focusing on their consistency with modular invariance and Hilbert space principles, and provides explicit one-loop partition functions and insights into higher-loop structures.

Contribution

It offers a detailed analysis of asymmetric orbifold models, emphasizing the interplay between fundamental consistency principles and deriving explicit partition functions.

Findings

Chiral reflection order must be 4 for consistency.

Explicit one-loop partition functions constructed.

Higher-loop partition functions built from symmetric orbifold blocks.

Abstract

Various asymmetric orbifold models based on chiral shifts and chiral reflections are investigated. Special attention is devoted to the consistency of the models with two fundamental principles for asymmetric orbifolds : modular invariance and the existence of a proper Hilbert space formulation for states and operators. The interplay between these two principles is non-trivial. It is shown, for example, that their simultaneous requirement forces the order of a chiral reflection to be 4, instead of the naive 2. A careful explicit construction is given of the associated one-loop partition functions. At higher loops, the partition functions of asymmetric orbifolds are built from the chiral blocks of associated symmetric orbifolds, whose pairings are determined by degenerations to one-loop.