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I am wondering if there are CFTs such that n-point correlation functions in them of the fields (may be the primaries or of some notion of twist fields) is exactly known.

  • Are there such?

  • Aren't minimal models supposed to have this property?

  • Even if not exactly known, can the n-point functions (may be when written as a conformal block expansion) be written order-by-order as a power series in the central charge? (..I guess there is some theorem about the asymptotic exponential dependence of the conformal blocks on the central charge (reference help? ) and I want to know if 1/c corrections to that are known..)

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Are your $n$-point correlation functions in genus zero? –  S. Carnahan Oct 13 '13 at 14:15
    
@S.Carnahan That would be the simplest scenario I would like to know of. (..if you can say something about higher genus then that is more exciting ;P..) –  user6818 Oct 13 '13 at 18:15
    
Did you look at the work of Dotsenko and Fateev from mid 1980s. They computed correlation functions of a number of 2d conformal field theories. –  José Figueroa-O'Farrill Oct 14 '13 at 19:33
    
@JoséFigueroa-O'Farrill Can you kindly refer to any paper that you have in mind? Is it known by some name that I can may be trace in the Francesco et. al's book? –  user6818 Oct 15 '13 at 17:05
    
@user6818, I have lent my copy of the book by di Francesco et al., I'm afraid, but the papers I have in mind are the following: dx.doi.org/10.1016%2F0550-3213%2884%2990269-4 and dx.doi.org/10.1016%2FS0550-3213%2885%2980004-3 . –  José Figueroa-O'Farrill Oct 15 '13 at 23:24
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