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arXiv · 1305.1321

Diagonal Limit for Conformal Blocks in d Dimensions

Matthijs Hogervorst·Hugh Osborn·Slava Rychkov
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Abstract

Conformal blocks in any number of dimensions depend on two variables z, zbar. Here we study their restrictions to the special "diagonal" kinematics z = zbar, 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 3F2 functions.

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Matthijs Hogervorst, Hugh Osborn, Slava Rychkov. 2015-10-28. Diagonal Limit for Conformal Blocks in d Dimensions. https://doi.org/10.1007/jhep08(2013)014

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