# E(lementary) Strings in Six-Dimensional Heterotic F-Theory

## TL;DR

This paper explores the role of E-strings in analyzing six-dimensional superconformal theories, heterotic vacua, and string combinations, revealing their fundamental importance in string theory constructions and anomaly cancellations.

## Contribution

It introduces the concept of elementary E-strings and demonstrates their role in forming various string types and constructing 6D theories, including D- and E-type models.

## Key findings

- E-strings can form M-strings, heterotic strings, and G-strings.
- Most 6D superconformal theories arise from heterotic small instanton emissions and combinations.
- Anomaly cancellation conditions are expressed in terms of elementary E-string combinations.

## Abstract

Using E-strings, we can analyze not only six-dimensional superconformal field theories but also probe vacua of non-perturabative heterotic string. We study strings made of D3-branes wrapped on various two-cycles in the global F-theory setup. We claim that E-strings are elementary in the sense that various combinations of E-strings can form M-strings as well as heterotic strings and new kind of strings, called G-strings. Using them, we show that emissions and combinations of heterotic small instantons generate most of known six-dimensional superconformal theories, their affinizations and little string theories. Taking account of global structure of compact internal geometry, we also show that special combinations of E-strings play an important role in constructing six-dimensional theories of $D$- and $E$-types. We check global consistency conditions from anomaly cancellation conditions, both from five-branes and strings, and show that they are given in terms of elementary E-string combinations.