Diagonal limit for conformal blocks in d dimensions

作者：Hogervorst Matthijs^*; O**orn Hugh; Rychkov Slava

来源：The Journal of High Energy Physics, 2013, 2013(8): 014.

DOI：10.1007/JHEP08(2013)014

• Conformal and W Symmetry
• Field Theories in Higher Dimensions

Conformal blocks in any number of dimensions depend on two variables z, (z) over bar. Here we study their restrictions to the special "diagonal" kinematics z = (z) over bar, 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 F-3(2) functions.

• 出版日期2013-8