  We consider Yang-Mills theory with a matrix gauge group $G$ on a direct
product manifold $M=\Sigma_2\times H^2$, where $\Sigma_2$ is a two-dimensional
Lorentzian manifold and $H^2$ is a two-dimensional open disc with the boundary
$S^1=\partial H^2$. The Euler-Lagrange equations for the metric on $\Sigma_2$
yield constraint equations for the Yang-Mills energy-momentum tensor. We show
that in the adiabatic limit, when the metric on $H^2$ is scaled down, the
Yang-Mills equations plus constraints on the energy-momentum tensor become the
equations describing strings with a worldsheet $\Sigma_2$ moving in the based
loop group $\Omega G=C^\infty (S^1, G)/G$, where $S^1$ is the boundary of
$H^2$. By choosing $G=R^{d-1, 1}$ and putting to zero all parameters in $\Omega
R^{d-1, 1}$ besides $R^{d-1, 1}$, we get a string moving in $R^{d-1, 1}$. In
arXiv:1506.02175 it was described how one can obtain the Green-Schwarz
superstring action from Yang-Mills theory on $\Sigma_2\times H^2$ while $H^2$
shrinks to a point. Here we also consider Yang-Mills theory on a
three-dimensional manifold $\Sigma_2\times S^1$ and show that in the limit when
the radius of $S^1$ tends to zero, the Yang-Mills action functional
supplemented by a Wess-Zumino-type term becomes the Green-Schwarz superstring
action.
