Free Field Realization of $\mathcal{W}$-Algebra Associated with Exceptional Lie Algebras

Daichi Ide, Katsushi Ito, Shigeki Miyazaki

We study the free field realization of the $\mathcal{W}$-algebra associated with the exceptional Lie algebras $E_6$, $E_7$, $E_8$, and $F_4$. We develop a recursive construction in…