$W_\infty$ and Anomalies of Self-Dual Einstein Theories
This manuscripts corrects some minor error in the paper, Mod. Phys. Lett. A 6 1893 (1991)
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arXiv subjects
V. G. J. Rodgers
Publications and source records attributed to V. G. J. Rodgers.
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 $W_2$ and $w_\infty$ 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 $\hbar$ contributions to gravity which can be associated with the $W_2$ anomaly. We comment on the relationship to gravitational monopoles.
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QCD Instantons and 2D Surfaces
Some time ago, Atiyah showed that there exists a natural identification between the k-instantons of a Yang-Mills theory with gauge group $G$ and the holomorphic maps from $CP_1$ to $ΩG$. Since then, Nair and Mazur, have associated the $Θ$ vacua structure in QCD with self-intersecting Riemann surfaces immersed in four dimensions. From here they concluded that these 2D surfaces correspond to the non-perturbative phase of QCD and carry the topological information of the $Θ$ vacua. In this paper we would like to elaborate on this point by making use of Atiyah's identification. We will argue that an effective description of QCD may be more like a $WZW$ model coupled to the induced metric of an immersion of a 2-D Riemann surface in $R^4$. We make some further comments on the relationship between the coadjoint orbits of the Kac-Moody group on $G$ and instantons with axial symmetry and monopole charge.
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