Topological Mass Generation in Four Dimensions

We show that in a large class of physically interesting systems the mass-generation phenomenon can be understood in terms of topological structures, without requiring a detailed knowledge of the underlying dynamics. This is first demonstrated by showing that Schwinger’s mechanism for mass generation relies on topological structures of a two-dimensional gauge theory. In the same manner, corresponding four-dimensional topological entities give rise to topological mass generation in four dimensions. This formulation offers a unified topological description of some seemingly unrelated phenomena, such as two-dimensional superconductivity, and the generation of ${\eta }^{\prime }$ and axion masses by QCD, and possibly by gravity.

Figure 1

Anomaly diagram that correlates ${\mathcal{C}}_4^{\alpha }$ and ${\mathcal{J}}_{\beta }^5$.