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arXiv · 2212.05311

Back to Heterotic Strings on ALE Spaces: Part II -- Geometry of T-dual Little Strings

Michele Del Zotto·Muyang Liu·Paul-Konstantin Oehlmann
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Abstract

This work is the second of a series of papers devoted to revisiting the properties of Heterotic string compactifications on ALE spaces. In this project we study the geometric counterpart in F-theory of the T-dualities between Heterotic ALE instantonic Little String Theories (LSTs) extending and generalising previous results on the subject by Aspinwall and Morrison. Since the T-dualities arise from a circle reduction one can exploit the duality between F-theory and M-theory to explore a larger moduli space, where T-dualities are realised as inequivalent elliptic fibrations of the same geometry. As expected from the Heterotic/F-theory duality the elliptic F-theory Calabi-Yau we consider admit a nested elliptic K3 fibration structure. This is central for our construction: the K3 fibrations determine the flavor groups and their global forms, and are the key to identify various T-dualities. We remark that this method works also more generally for LSTs arising from non-geometric Heterotic backgrounds. We study a first example in detail: a particularly exotic class of LSTs which are built from extremal K3 surfaces that admit flavor groups with maximal rank 18. We find all models are related by a so-called T-hexality (i.e. a 6-fold family of T-dualities) which we predict from the inequivalent elliptic fibrations of the extremal K3.

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Michele Del Zotto, Muyang Liu, Paul-Konstantin Oehlmann. 2023-10-17. Back to Heterotic Strings on ALE Spaces: Part II -- Geometry of T-dual Little Strings. https://arxiv.org/abs/2212.05311

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