Lie algebra lattices and strings on T-folds

Abstract

We study the world-sheet conformal field theories for T-folds systematically based on the Lie algebra lattices representing the momenta of strings. The fixed point condition required for the T-duality twist restricts the possible Lie algebras. When the T-duality acts as a simple chiral reflection, one is left with the four cases, $A_1,D_{2r},E_7,E_8$, among the simple simply-laced algebras. From the corresponding Englert-Neveu lattices, we construct the modular invariant partition functions for the T-fold CFTs in bosonic string theory. Similar construction is possible also by using Euclidean even self-dual lattices. We then apply our formulation to the T-folds in the $E_8\times E_8$ heterotic string theory. Incorporating non-trivial phases for the T-duality twist, we obtain, as simple examples, a class of modular invariant partition functions parametrized by three integers. Our construction includes the cases which are not reduced to the free fermion construction.

arXiv comment32 pages, no figures

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Cited by in corpus (7)

• GUT Precursors and Entwined SUSY: The Phenomenology of Stable Non-Supersymmetric Strings
• T-duality orbifolds of heterotic Narain compactifications
• An Uplifting Discussion of T-Duality
• A Worldsheet Perspective on Heterotic T-Duality Orbifolds
• Notes on Vanishing Cosmological Constant without Bose-Fermi Cancellation
• Interactions of strings on a T-fold
• Non-supersymmetric D-branes with Vanishing Cylinder Amplitudes in Asymmetric Orbifolds