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N=2 S-duality via Outer-automorphism Twists

Yuji Tachikawa

TL;DR

The paper develops twisted compactifications of the 6d $\mathcal{N}=(2,0)$ theory of type $D_N$ using outer-automorphism twists to generate new 4d $\mathcal{N}=2$ S-dualities. By placing the 6d theory on punctured Riemann surfaces and employing $\mathbb{Z}_s$ twists (notably $\mathbb{Z}_3$ for $D_4$), the author constructs dual pairs in which Lagrangian gauge sectors couple to strongly interacting SCFTs such as the Minahan–Nemeschansky $E_7$ theory, e.g., relating $SO(8)$ with three $\mathbf{8}$ hypers to a $G_2$ theory with two $E_7$ MN sectors. A Higgs-branch move (replacing a puncture) yields a second dual pair involving $SO(7)$ and $G_2$ with MN sectors, reproducing Argyres–Wittig’s Example 9. These results demonstrate a systematic route to richer S-duality webs and isolated SCFTs via twisted 6d constructions, suggesting a broader catalog of dualities accessible through outer-automorphism twists. The work integrates punctured-surface data, differential structures, and Higgsing to map between distinct 4d theories, highlighting the role of $E_7$ and $G_2$ sectors in these dualities.

Abstract

Compactification of 6d N=(2,0) theory of type G on a punctured Riemann surface has been effectively used to understand S-dualities of 4d N=2 theories. We can further introduce branch cuts on the Riemann surface across which the worldvolume fields are transformed by the discrete symmetries associated to those of the Dynkin diagram of type G. This allows us to generate more S-dualities, and in particular to reproduce a couple of S-dual pairs found previously by Argyres and Wittig.

N=2 S-duality via Outer-automorphism Twists

TL;DR

The paper develops twisted compactifications of the 6d theory of type using outer-automorphism twists to generate new 4d S-dualities. By placing the 6d theory on punctured Riemann surfaces and employing twists (notably for ), the author constructs dual pairs in which Lagrangian gauge sectors couple to strongly interacting SCFTs such as the Minahan–Nemeschansky theory, e.g., relating with three hypers to a theory with two MN sectors. A Higgs-branch move (replacing a puncture) yields a second dual pair involving and with MN sectors, reproducing Argyres–Wittig’s Example 9. These results demonstrate a systematic route to richer S-duality webs and isolated SCFTs via twisted 6d constructions, suggesting a broader catalog of dualities accessible through outer-automorphism twists. The work integrates punctured-surface data, differential structures, and Higgsing to map between distinct 4d theories, highlighting the role of and sectors in these dualities.

Abstract

Compactification of 6d N=(2,0) theory of type G on a punctured Riemann surface has been effectively used to understand S-dualities of 4d N=2 theories. We can further introduce branch cuts on the Riemann surface across which the worldvolume fields are transformed by the discrete symmetries associated to those of the Dynkin diagram of type G. This allows us to generate more S-dualities, and in particular to reproduce a couple of S-dual pairs found previously by Argyres and Wittig.

Paper Structure

This paper contains 7 sections, 13 equations, 6 figures.

Table of Contents

  1. Introduction and Discussions
  2. Review of the $D_N$ theory
  3. Worldvolume fields and punctures
  4. Sphere with ${\color{RED}\pmb\odot}$, $\hbox{$\bigstar$}$ and $\pmb{\times}$
  5. Sphere with ${\color{RED}\pmb\odot}$, $\hbox{$\heartsuit$}$ and $\pmb{\times}$
  6. First example
  7. Second example

Figures (6)

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  • ...and 1 more figures