I'm reading Polchinski and am confused about equation (1.3.13), $$\gamma_{\tau\sigma}\partial_\tau X^\mu-\gamma_{\tau\tau}\partial_\sigma X^\mu=0~~~~~\text{at}~~~~~\sigma=0,l.\tag{1.3.13}$$
It says that this comes from $$\partial^\sigma X^\mu(\tau,0)=\partial^\sigma X^\mu(\tau,l)=0\tag{1.3.15}$$ along with the gauge conditions $$\partial_\sigma\gamma_{\sigma\sigma}=0;~~~~~\det\gamma_{ab}=-1,\tag{1.3.8bc}$$ but I really don't see it. How does the metric come into play?