# Polchinski Vol.2 P58 projection under a twist with a discrete torsion in E8$\times$E8 superstring

I don't know how to get the projection Equation (11.3.15) in the book.

In the $$E_8\timesE_8$$ superstring theory, one can introduce the following twist,

$$(h_1,h_2)=(\exp[\pi i(k_1F_1+l_1\tilde{F})],\exp[\pi i(k_2F_1+l_2\tilde{F})])$$

which produces a phase, the discrete torsion,

$$\epsilon(h_1,h_2)=(-1)^{k_1l_2+k_2l_1}$$

This procedure modifies the original projection, the diagonal one, to,

$$\exp[\pi i(F_1+\alpha_1'+\tilde{\alpha})]=\exp[\pi i(F_1'+\alpha_1+\tilde{\alpha})]=\exp[\pi i(\tilde{F}+\alpha_1+\alpha_1')]=1\tag{11.3.15}$$

where $$F$$ is the worldsheet spinor number, $$\alpha$$ denote the sector, R or NS.

I see no reason how $$\alpha$$ enter the equation.