A Worldsheet Perspective on Heterotic T-Duality Orbifolds

TL;DR

This paper develops a worldsheet approach to heterotic T-duality orbifolds, connecting gauge fixing, generalized metrics, and orbifold actions to understand T-folds and moduli redefinitions.

Contribution

It introduces a worldsheet framework for heterotic T-duality orbifolds, including methods to construct invariant generalized metrics and analyze orbifold effects.

Findings

Derived a duality covariant description from Buscher's gauging

Outlined a method to obtain invariant generalized metrics under T-duality orbifolds

Constructed new higher-dimensional T-folds including a Z6 asymmetric orbifold

Abstract

Asymmetric heterotic orbifolds are discussed from the worldsheet perspective. Starting from Buscher's gauging of a theory of D compact bosons the duality covariant description of Tseytlin is obtained after a non-Lorentz invariant gauge fixing. A left-over of the gauge symmetry can be used to removed the doubled constant zero modes so that D physical target space coordinate remain. This can be thought of as the worldsheet realization of the strong constraint of double field theory. The extension of this description to the heterotic theory is straightforward as all results are written in terms of the invariant and the generalized metrics. An explicit method is outline how to obtain a generalized metric which is invariant under T-duality orbifold actions. It is explicitly shown how shift orbifolds lead to redefinitions of the Narain moduli. Finally, a number of higher dimensional T-folds are constructed including a novel asymmetric Z6 orbifold.