On the 6d origin of discrete additional data of 4d gauge theories

Understand

Starting with a choice of gauge algebras, specification of a 4d gauge theory involves additional data, namely the gauge groups and the discrete theta angles.

• Equivalently, one needs to specify the set of charges of allowed line operators.
• In this note, we study how these additional data are represented in 6d, when the 4d theory in question is an N=4 super Yang-Mills theory or an N=2 class S theory.
• We will see that the Z_N symmetry of the so-called T_N theory plays an important role.