2. Given $\boldsymbol{a}=\left(\cos \frac{2}{3} \pi, \sin \frac{2}{3} \pi\right), \overrightarrow{O A}=\boldsymbol{a}-$ $\boldsymbol{b}, \overrightarrow{O B}=\boldsymbol{a}+\boldsymbol{b}$, if $\triangle O A B$ is an isosceles right triangle with $O$ as the right-angle vertex, then the area of $\triangle O A B$ is $\qquad$