Conformal Field Theory and Algebraic Structure of Gauge Theory

We consider various homotopy algebras related to Yang-Mills theory and two-dimensional conformal field theory (CFT). Our main objects of study are Yang-Mills $L_{\mathrm{\infty }}$ and $C_{\mathrm{\infty }}$ algebras and their relation to the certain algebraic structures of Lian-Zuckerman type in CFT. We also consider several examples of algebras related to gauge theory, involving first order formulations and gauge theories with matter fields.