# 6D Heterotic Little String Theories and F-theory Geometry: An Introduction

**Authors:** Michele Del Zotto, Muyang Liu, Paul-Konstantin Oehlmann  
**arXiv:** [2303.13502](https://arxiv.org/abs/2303.13502)  
**Date:** 2023-03-23  
**Summary page:** https://www.summarizepaper.com/en/paper/2303.13502v1/

## Key points

- Michele Del Zotto, Muyang Liu, and Paul-Konstantin Oehlmann have been studying the geometric engineering of heterotic little string theories using F-theory.
- They build on previous work by Aspinwall and Morrison as well as Intrilligator and Blum to solve open questions in our understanding of 6D (1,0) theories and their symmetries.
- The systems they study correspond to non-compact elliptically fibered Calabi-Yau varieties that must have the structure of an elliptic K3 fibration.
- The K3 fiber plays a central role in determining the 6D flavor group and different T-dual LSTs via inequivalent elliptic fibration structures.
- The geometries they obtain are finer versions of Kulikov degenerations where the point where the K3 fiber degenerates is where the LST arises.
- This structure allows for checking field theory predictions on LST dualities and deducing novel LST models and their networks of dualities, thus exploring non-geometric Heterotic regimes.
- Their findings provide insight into several aspects of heterotic little string theories that were previously not well understood.
- This work represents a significant contribution to our understanding of heterotic little string theories and provides a framework for further exploration into non-geometric Heterotic regimes.

## Summary

In their recent works, Michele Del Zotto, Muyang Liu, and Paul-Konstantin Oehlmann delve into the geometric engineering of heterotic little string theories using F-theory. They build on the seminal work by Aspinwall and Morrison as well as Intrilligator and Blum to solve some longstanding open questions thanks to recent progress in our understanding of 6D (1,0) theories and their generalized symmetries. On the geometry side, these systems correspond to non-compact elliptically fibered Calabi-Yau varieties that must admit the structure of an elliptic K3 fibration. From fiberwise F-theory/Heterotic duality, the K3 plays a central role - it determines the 6D flavor group, as well as different T-dual LSTs via inequivalent elliptic fibration structures. The geometries they obtain are some finer versions of Kulikov degenerations: the point where the K3 fiber degenerates is the locus where the LST arises. This structure serves on one hand to check field theory predictions on LST dualities via the match of Coulomb branch dimension, flavor symmetries, and 2-group structure constants. On the other hand, it allows for deducing novel LST models and their networks of dualities thus allowing exploring non-geometric Heterotic regimes. The authors' findings provide insight into several aspects of heterotic little string theories that were previously not well understood. By leveraging recent advances in our understanding of 6D (1,0) theories and their generalized symmetries along with fiberwise F-theory/Heterotic duality techniques, they have been able to make significant strides in this area. Overall, this work represents a significant contribution to our understanding of heterotic little string theories and provides a framework for further exploration into non-geometric Heterotic regimes.