The M-theory origin of global properties of gauge theories

Understand

We show that global properties of gauge groups can be understood as geometric properties in M-theory.

• Different wrappings of a system of N M5-branes on a torus reduce to four-dimensional theories with $A_{N-1}$ gauge algebra and different unitary groups.
• The classical properties of the wrappings determine the global properties of the gauge theories without the need to impose any quantum conditions.
• We count the inequivalent wrappings as they fall into orbits of the modular group of the torus, which correspond to the S-duality orbits of the gauge theories.