QCD in Large Colour Limit and Topological Skyrme Model with Wess-Zumino Anomaly Term

The Standard Model (SM) of particle physics has been very successful. However in it, the electric charge is not quantized and is fixed by hand to be 2/3 and -1/3. This is its major shortcoming. This model runs into conflict with another similarly structured, but actually quite different model, call it Quantized Charge Standard Model (QCSM), wherein the electric charge is fully quantized and depends upon colour degree of freedom as well. We study this basic conflict between these two models, and how they connect to a consistent study of Quantum Chromodynamics (QCD) for arbitrary number of colours. There arises the basic issue of consistency of Quantum Electrodynamics (QED) with these fundamentally different charges. Study of consistency of (QCD + QED) together, makes discriminating and conclusive statements about the relevance of these two model structures. QCD in large colour limit provides a natural passage to the Topological Skyrme model. However on quantization, one is forced to include a Wess-Zumino anomaly term in the Lagrangian. In order to understand connection with the above charge quantization, we study the structure of electric charge quantization in the Skyrme-Wess-Zumino model. We find that this provides clear statements as to which representations are allowed for two- and three- flavours.