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,


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.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.