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

TL;DR

This paper explores how BF theories arise from W-algebras and their relation to QCD, 4D gravity, and monopole solutions, revealing new connections between algebraic structures and physical theories.

Contribution

It demonstrates that BF theories naturally emerge from coadjoint orbits of W-algebras and links these to QCD strings and quantum gravity via Ashtekar variables.

Findings

BF theories from W-algebras include a Kac-Moody sector

QCD strings relate to BF theory and monopole solutions

Order al contributions to gravity linked to W_2 anomaly

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