T-duality Twists and Asymmetric Orbifolds

TL;DR

This paper investigates asymmetric orbifolds of tori involving T-duality group elements, clarifying how phase factors influence string theory consistency and modular invariance in toroidal compactifications.

Contribution

It provides a detailed analysis of T-duality twist phase factors and their impact on the symmetry, locality, and modular covariance of asymmetric orbifold theories.

Findings

Phase factors are linked to symmetry and locality of vertex operators.

Clarified the role of T-duality twists in modular covariance.

Applied analysis to orbifolds of root lattice tori.

Abstract

We study some aspects of asymmetric orbifolds of tori, with the orbifold group being some $\mathbb{Z}_N$ subgroup of the T-duality group and, in particular, provide a concrete understanding of certain phase factors that may accompany the T-duality operation on the stringy Hilbert space in toroidal compactification. We discuss how these T-duality twist phase factors are related to the symmetry and locality properties of the closed string vertex operator algebra, and clarify the role that they enact in the modular covariance of the orbifold theory, mainly using asymmetric orbifolds of tori which are root lattices as working examples.