2-Group Symmetries of 6d Little String Theories and T-duality

TL;DR

This paper calculates the 2-group structure constants for 6d little string theories engineered via F-theory, using these results to verify T-duality consistency, including cases with discrete symmetry twists.

Contribution

It provides the first geometric determination of 2-group structures for all 6d LSTs and uses these to test T-duality relations.

Findings

2-group structure constants are computed for all 6d LSTs.

T-duality pairs exhibit matching 2-group structures.

Discrete symmetry twists modify the 2-group matching in T-duality.

Abstract

We determine the 2-group structure constants for all the six-dimensional little string theories (LSTs) geometrically engineered in F-theory without frozen singularities. We use this result as a consistency check for T-duality: the 2- groups of a pair of T-dual LSTs have to match. When the T-duality involves a discrete symmetry twist the 2-group used in the matching is modified. We demonstrate the matching of the 2-groups in several examples.