Non-BPS Branes in a Type I Orbifold

We analyse the spectrum of non-BPS branes in the type I theory on the orbifold $T^4\mathrm{/}{\mathcal{I}}_4$. We present a detailed analysis of the action of the worldsheet parity $\mathrm{\Omega }$ on the different D-brane boundary state sectors of type IIB on $T^4\mathrm{/}{\mathcal{I}}_4$, using the covariant formulation. Using these results we derive the spectrum of branes in the type I orbifold. We find ${\mathbb{Z}}_2$- and $\mathbb{Z}$- charged non-BPS branes. A study of the stability of these branes in the type I orbifold is also presented. We find that the type I non-BPS D-particle and D-instanton remain stable in the orbifold. The D-particle carries no charge whereas the non-BPS D-instanton can carry twisted R-R charge.