# Derivation of KLT relations

The KLT relations (Kawai, Lewellen, Tye) relate a closed string amplitude to a product of open ones. While I get the physics behind this I don't really understand the derivation in the original paper (see http://www.sciencedirect.com/science/article/pii/0550321386903627 ). Especially I don't understand the contour deformations starting around eq 3.4 and following. I'd be glad if someone could either explain that a bit more in detail or point to a reference where this is done in all gory detail :)

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The paper is freely available in the KEK library: ccdb5fs.kek.jp/cgi-bin/img/allpdf?198511415 - And for the OP: could you please be more specific about what you don't understand? The paper is supposed to be self-explanatory and you surely don't want anyone to write a longer version of that paper here. –  Luboš Motl Apr 8 '13 at 17:47
@Lubos: Thanks for the link. What I'm interested in is specifically the derivation of the phase factor (3.8). They do this by considering branch cuts of the integrand as they explain in words before. But just from those words I can't reconstruct precisely what they do. I tried to rederive their phase factor but then I don't see how they do it and moreover I can't reproduce figure 2 which is not in the KEK version unfortunately. –  A friendly helper Apr 8 '13 at 18:05
Dear Friendly Helper, the figures are at the end of the scanned PDF document. –  Luboš Motl Apr 8 '13 at 18:08
@Lubos: Ups, my bad :) –  A friendly helper Apr 8 '13 at 19:21