2d orbifolds with exotic supersymmetry

We analyse various two dimensional theories arising from compactification of type II and heterotic string theory on asymmetric orbifolds. We find extra supersymmetry generators arising from twisted sectors, giving rise to exotic supersymmetry algebras. Among others we discover new cases with a large number of supercharges, such as $ \mathcal{N}=\left(20,8\right),\ \mathcal{N}=\left(24,8\right),\ \mathcal{N}=\left(32,0\right),\ \mathcal{N}=\left(24,24\right) $ and $ \mathcal{N}=\left(48,0\right) $ .