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

In the $E_8$$\times$$E_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.

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