The M-theory origin of global properties of gauge theories

TL;DR

This paper demonstrates that the global properties of gauge groups in four-dimensional theories can be derived from geometric configurations in M-theory, specifically from the wrappings of M5-branes on a torus, linking geometry to gauge theory characteristics.

Contribution

It provides a geometric understanding of gauge group global properties via M-theory brane wrappings, eliminating the need for quantum conditions.

Findings

Global properties correspond to geometric wrappings in M-theory.

Inequivalent wrappings form orbits under the torus's modular group.

These orbits match the S-duality classes of gauge theories.

Abstract

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.