Brane mapping under $(-1)^{F_L}$
We present the evidence that $(-1)^{F_L}$ is a nonperturbative symmetry of Type II string theory. We argue that $(-1)^{F_L}$ is a symmetry of string theory as much as the $SL(2, Z)$ of the Type II string is and how the branes are mapped under the $(-1)^{F_L}$ modding. NS branes are mapped into the NS branes with the same world volume dimensions but with the different chiral structure. Supersymmetric Dp-branes (bound with anti-Dp branes) are mapped to unstable nonsupersymmetric Dp-branes, which has D(p-1)-branes as kink solutions according to Horava.