How does the worldsheet turn spacetime vectors into spinors in string theory?

[selfAdjoint]

In Cumrun Vafa's "Lightning Introduction" to string theory in his http://arxiv.org/hep-th/9702201 , he instroduces supersymmetry to string theory thus:

in addition to the coordinates $$X^{\mu}$$ we also have anti-commuting fermionic coordinates $$\psi_{L,R}^{\mu}$$ which are spacetime vectors but fermionic spinors on the worldsheet whose chirality is denoted by subscript L, R.


I have no problem with the anti-commutative coordinates themselve, but how does the worldsheet make vectors in spacetime appear as spinors?

 

[marcus]

In Cumrun Vafa's "Lightning Introduction" to string theory in his http://archive.org/hep-th/9702201 , he instroduces supersymmetry to string theory thus:

in addition to the coordinates $$X^{\mu}$$ we also have anti-commuting fermionic coordinates $$\psi_{L,R}^{\mu}$$ which are spacetime vectors but fermionic spinors on the worldsheet whose chirality is denoted by subscript L, R.




I have no problem with the anti-commutative coordinates themselve, but how does the worldsheet make vectors in spacetime appear as spinors?

darnit selfAdjoint, you spelled arxiv wrong so the link does not work

http://archive.org/hep-th/9702201

make it
http://arxiv.org/hep-th/9702201

 

[selfAdjoint]

Sorry about that. It's fixed now.