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

Michele Del Zotto, Kantaro Ohmori

TL;DR

The work provides a universal, geometry-driven method to compute 2-group global symmetry data for all 6d LSTs engineered in F-theory, encapsulating the LS charge and Green–Schwarz couplings into compact structure constants. It demonstrates that untwisted T-dual LST pairs have matching 2-group constants, and that twisted T-dualities modify this matching in a controlled way via the orbit structure of tensor multiplets and fractional Little String charges. The paper also identifies an endpoint-based invariant for κ_P, clarifying a T-duality constraint, and develops a formalism for twisted T-dualities, including explicit non-simply laced examples. Together, these results provide a robust consistency check for proposed LST T-dualities and illuminate how higher-form symmetries constrain duality webs in 6d theories.

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.

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

TL;DR

The work provides a universal, geometry-driven method to compute 2-group global symmetry data for all 6d LSTs engineered in F-theory, encapsulating the LS charge and Green–Schwarz couplings into compact structure constants. It demonstrates that untwisted T-dual LST pairs have matching 2-group constants, and that twisted T-dualities modify this matching in a controlled way via the orbit structure of tensor multiplets and fractional Little String charges. The paper also identifies an endpoint-based invariant for κ_P, clarifying a T-duality constraint, and develops a formalism for twisted T-dualities, including explicit non-simply laced examples. Together, these results provide a robust consistency check for proposed LST T-dualities and illuminate how higher-form symmetries constrain duality webs in 6d theories.

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.

Paper Structure

This paper contains 16 sections, 72 equations, 1 table.

Table of Contents

  1. Abstract
  2. Introduction
  3. LST from F-theory: a lightning review
  4. 2-group structure constants and the LS charge
  5. 2-groups and T-duality
  6. T-duality from geometric engineering
  7. $\mathcal{N}=(2,0)$ and its T-dual $\mathcal{N}=(1,1)$
  8. LST for M5 branes along $S^1 \times \mathbb C^2/\Gamma$ and their T-duals
  9. Heterotic instantons probing a $\mathbb C^2 / \mathbb Z_k$ singularity
  10. Heterotic instantons probing an $E_6$ singularity
  11. An endpoint constraint for T-duality from $\widehat{\kappa}_\mathscr{P}$
  12. Twisted T-dualities and 2-group structure
  13. A motivating example
  14. Twisting and 2-group structure constants
  15. Twisted T-duality and non-simply laced 6d $(1,1)$ LSTs
  16. ...and 1 more sections