 Light-cone coordinates

For mostly-plus signature, $x^{+}=(x^{D-1}+x^0)/\sqrt{2}$ and $x^{-}=(x^{D-1}-x^0)/\sqrt{2}$ give $d{s}^2=2d{x}^{+}d{x}^{-}+d{x}^{I}d{x}^I$. In this convention raising a plus or minus derivative exchanges the two labels.