Applications of W algebras to BF theories, QCD and 4D gravity

In this paper, the authors 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, the authors observe that when 4D gravitation is cast into a BF form through the use of Ashtekar variables the authors are able to get order Λ contributions to gravity which can be associated with the W2 anomaly. The authors comment on the relationship to gravitational monopoles