Diagonal limit for conformal blocks in \(d\) dimensions
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Publication:737484
DOI10.1007/JHEP08(2013)014zbMATH Open1342.81497arXiv1305.1321MaRDI QIDQ737484
Author name not available (Why is that?)
Publication date: 12 August 2016
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/1305.1321
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