The Effects of Topology in the Standard Model: Quantum Chromodynamics and the Strong CP Problem

Synopsis

The Lagrangian formulation of field theories is an incredibly powerful tool with both classical and quantum applications. Often in physics we consider systems with trivial topology, but what happens to the Action functional when the space and fields are topologically non-trivial? In this talk I will discuss a major open question in the field of Quantum Chromodynamics (QCD): The theory of QCD seems able to violate Charge-Parity (CP) Symmetry. However, experimentally we observe no such CP violation. While the non-observation of CP violation is an open question, I will focus on the Lagrangian itself.  The presence of the CP violating Lagrangian term is quite fascinating, as it is intimately related to the non-trivial topology of the QCD gauge group. To better understand the situation, I will present a 1D toy topological example and show how the Action can "feel" the space and field topology. I hope to show the motivation for the fundamentals of the Strong CP Problem, which leads to an open area of research, including the hypothetical particle, the Axion.