Applications of W Algebras to BF Theories, QCD, and 4D Gravity

We are able to show that BF theories naturally emerge from the coadjoint orbits of W2 and w∞ algebras which includes a Kac-Moody sector. Since QCD strings can be identified with a BF theory, we are able to show a relationship between the orbits and monopole-string solutions of QCD. Furthermore, we observe that when 4D gravitation is cast into a BF form through the use of Ashtekar variables, we are able to get order ¯ contributions to gravity which can be associated with the W2 anomaly. We comment on the relationship to gravitational monopoles.