Diagonal Limit for Conformal Blocks in d Dimensions
High Energy Physics - Theory
2015-10-30 v3
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.
Keywords
Cite
@article{arxiv.1305.1321,
title = {Diagonal Limit for Conformal Blocks in d Dimensions},
author = {Matthijs Hogervorst and Hugh Osborn and Slava Rychkov},
journal= {arXiv preprint arXiv:1305.1321},
year = {2015}
}
Comments
21 pages; v2: misprints in Eqs. 2.17 and 4.9 corrected; v3: misprints in A.5 and A.6 corrected