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Apologies in advance for what will surely sound like a, "well why can't you just Google it" question, but I'm struggling to find good literature that presents the basic construction of genus two partition functions (or honestly, really good literature on genus one partition functions). I'm looking within the context of conformal field theories, an interested in the geometric expressions, but I can not seem to find papers that aren't dense in jargon. It's not my field, so I don't know who the go-to authors here are, and I want something that doesn't just assume that I know exactly which path integral methods they mean or why a 'central charge 24 bosonic string' is something I might lose sleep over (with or without Moonshine).

I'll appreciate any recommendations/starting places.

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Eric D'Hoker and D. H. Phong have written a series of 7 papers on two-loop superstring amplitudes (available on the arXiv). Those papers might be useful, but don't sound like exactly what you want. Phong is a mathematician at Columbia and if you contact him he might be able to point you in the right direction for genus two amplitudes with more of a CFT emphasis. –  Jeff Harvey Feb 4 '11 at 4:56
    
It might help to know what your field is. –  JSE Feb 4 '11 at 7:09
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I like the discussion in math/9910136. –  Mitchell Porter Feb 4 '11 at 9:19
    
You could try Blumenhagen, Ralph; Plauschinn, Erik: "Introduction to conformal field theory. With applications to string theory." Chapter four is an introduction to CFT on the torus. Genus two is not handled in this book, AFAIK, however. –  Tim van Beek Feb 4 '11 at 11:21

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