Worldsheet stress-energy tensor ($T_{ab}$)

Varying the independent worldsheet metric gives $T_{ab}=T[{\partial }_{a}X\cdot {\partial }_{b}X-\frac{1}{2}{\gamma }_{ab}{\gamma }^{cd}{\partial }_{c}X\cdot {\partial }_{d}X]$. Its classical vanishing is the metric equation and produces the Virasoro constraints.