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By S. Forste

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16), both in the second half (17, . . , 32), or one of them out of the first half and the other one out of the second half. So far, this gave only a rearrangement of those states. But now we impose the GSO projection such that only states survive where an even number of fermionic left moving creators act in each half separately. This removes the (16, 16) combination. Further, when we split the range of indices into two groups of 16 each, there will be additional massless states. It is simple to check that in the sector where half of the boundary conditions are periodic and the other half is anti-periodic (the AP or PA sector), the left moving normal ordering constant vanishes.

Analogously the second diagram contains four vertices and so on. Assigning to each vertex one power of the string coupling gs , this gives a formal 2. Perturbative expansion and effective actions + 37 +... 3: Perturbative expansion of the four point function in a string computation power series A= ∞ n=0 gs2n+2 A(n) . 1) This power series can be truncated after the first contributions as long as gs 1. It remains to specify what gs is. 1) is nothing but minus the Euler number of a worldsheet with n handles and four boundaries.

The bosonic string on an orbicircle State αi−1 |0 α25 −1 |0 Z2 + − 52 24 + 1 dim. rep. 4: Untwisted right moving states which is invariant under the orbifold projection x25 → −x25 . Since in the bosonic string the right moving sector is identical to the left moving one, we first write down the right moving states only. 4 (i = 2, . . , 24; the zeroth and first direction are eliminated by the light-cone gauge). Now we need to combine left with right movers such that the resulting state is invariant under the Z2 .

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