Gauging discrete symmetries of TN-theories in five dimensions

A bstract We study the gauging of a discrete 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 × SU( N ) or SU(3) × SU( N ) global symmetry group. In the M -theory realisation of T N theories as residing at the origin in the Calabi-Yau orbifolds C³ZN× ZN ℂ3ℤN×ℤN we identify the ℤ 3 symmetry geometrically and the new theories arise from M -theory on the non-Abelian orbifolds (C³ZN× ZN)/Z₃ ℂ3ℤN×ℤN/ℤ3 . 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.