Abstract
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.
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Acharya, B., Lambert, N., Najjar, M. et al. Gauging discrete symmetries of TN-theories in five dimensions. J. High Energ. Phys. 2022, 114 (2022). https://doi.org/10.1007/JHEP04(2022)114
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DOI: https://doi.org/10.1007/JHEP04(2022)114