Gauging Discrete Symmetries of $T_N$-theories in Five Dimensions

TL;DR

This paper explores the gauging of a discrete $bZ_3$ symmetry in 5D $T_N$ superconformal theories, leading to new theories with enhanced global symmetries, using M-theory and brane web descriptions.

Contribution

It introduces a novel gauging of a $bZ_3$ symmetry in 5D $T_N$ theories, resulting in an infinite sequence of new superconformal theories with specific global symmetries.

Findings

Identification of the $bZ_3$ symmetry in M-theory orbifolds.

Construction of new theories via non-Abelian orbifolds.

Manifestation of $E_6$ symmetry in $U$-fold backgrounds.

Abstract

We study the gauging of a discrete $\mathbb{Z}_3$ symmetry in the five-dimensional superconformal $T_N$ theories. We argue that this leads to an infinite sequence of five-dimensional superconformal theories with either $E_6 \times SU(N)$ or $SU(3)\times SU(N)$ global symmetry group. In the $M$-theory realisation of $T_N$ theories as residing at the origin in the Calabi-Yau orbifolds ${\mathbb{C}^3 \over {\mathbb{Z}_N \times \mathbb{Z}_N}}$ we identify the $\mathbb{Z}_3$ symmetry geometrically and the new theories arise from $M$-theory on the non-Abelian orbifolds $({\mathbb{C}^3 \over {\mathbb{Z}_N \times \mathbb{Z}_N}})/{\mathbb{Z}_3}$. On the other hand, in the $(p,q)$ 5-brane web description in Type IIB theory, the symmetry combines the $U$-duality symmetry with a rotation in space, defining a so-called $U$-fold background, where the $E_6$ symmetry is manifest.