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

Abstract

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 $\hslash$ contributions to gravity which can be associated with the $W_2$ anomaly. We comment on the relationship to gravitational monopoles.

14 pages

References in corpus (1)

• QCD Instantons and 2D Surfaces

Cited by in corpus (7)

• Yang-Mills, Gravity, and String Symmetries
• A Study of Fermions Coupled to Gauge and Gravitational Fields on a Cylinder
• Interactions of a String Inspired Graviton Field
• A 2D Inspired 4D Theory of Gravity
• A Geometric Action for the Courant Bracket
• General Coordinate Transformations as the Origins of Dark Energy
• Diffeomorphisms as quadratic charges in 4d BF theory and related TQFTs