On the String Actions for the Generalized Two-dimensional Yang-Mills Theories

We study the structures of partition functions of the large $N$ generalized two-dimensional Yang-Mills theories ($gYM_2$) by recasting the higher Casimirs. We clarify the appropriate interpretations of them and try to extend the Cordes-Moore-Ramgoolam's topological string model describing the ordinary $YM_2$ \cite{CMR} to those describing $gYM_2$. We present the expressions of the appropriate operators to reproduce the higher Casimir terms in $gYM_2$. The concept of ''deformed gravitational descendants'' will be introduced for this purpose.