Abstract
Conformal blocks in any number of dimensions depend on two variables z, \( \overline{z} \). Here we study their restrictions to the special “diagonal” kinematics \( z=\overline{z} \), previously found useful as a starting point for the conformal bootstrap analysis. We show that conformal blocks on the diagonal satisfy ordinary differential equations, third-order for spin zero and fourth-order for the general case. These ODEs determine the blocks uniquely and lead to an efficient numerical evaluation algorithm. For equal external operator dimensions, we find closed-form solutions in terms of finite sums of 3 F 2 functions.
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ArXiv ePrint: 1305.1321
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Hogervorst, M., Osborn, H. & Rychkov, S. Diagonal limit for conformal blocks in d dimensions. J. High Energ. Phys. 2013, 14 (2013). https://doi.org/10.1007/JHEP08(2013)014
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DOI: https://doi.org/10.1007/JHEP08(2013)014