Gauging discrete symmetries of TN-theories in five dimensions

We study the gauging of a discrete ℤ3 symmetry in the five-dimensional superconformal TN theories. We argue that this leads to an infinite sequence of five-dimensional superconformal theories with either E6 × SU(N) or SU(3) × SU(N) global symmetry group. In the M-theory realisation of TN theories as residing at the origin in the Calabi-Yau orbifolds $$ \frac{{\mathbb{C}}^3}{{\mathbb{Z}}_N\times {\mathbb{Z}}_N} $$ we identify the ℤ3 symmetry geometrically and the new theories arise from M-theory on the non-Abelian orbifolds $$ \left(\frac{{\mathbb{C}}^3}{{\mathbb{Z}}_N\times {\mathbb{Z}}_N}\right)/{\mathbb{Z}}_3 $$ . 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 E6 symmetry is manifest.