Gauging discrete symmetries of TN-theories in five dimensions
B. S. Acharya, Neil Lambert, Marwan Najjar, Eirik Eik Svanes, Jiahua Tian
Abstract
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 $$ \frac{{\mathbb{C}}^3}{{\mathbb{Z}}_N\times {\mathbb{Z}}_N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mfrac><mml:msup><mml:mi>ℂ</mml:mi><mml:mn>3</mml:mn></mml:msup><mml:mrow><mml:msub><mml:mi>ℤ</mml:mi><mml:mi>N</mml:mi></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mi>ℤ</mml:mi><mml:mi>N</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:math> we identify the ℤ 3 symmetry geometrically and the new theories arise from M -theory on the non-Abelian orbifolds $$ \left(\frac{{\mathbb{C}}^3}{{\mathbb{Z}}_N\times {\mathbb{Z}}_N}\right)/{\mathbb{Z}}_3 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mfenced><mml:mfrac><mml:msup><mml:mi>ℂ</mml:mi><mml:mn>3</mml:mn></mml:msup><mml:mrow><mml:msub><mml:mi>ℤ</mml:mi><mml:mi>N</mml:mi></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mi>ℤ</mml:mi><mml:mi>N</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mfenced><mml:mo>/</mml:mo><mml:msub><mml:mi>ℤ</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math> . 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.