JHEP, 11, 135 (2021)
Hidden relations of central charges and OPEs in holographic CFT
Yue-Zhou Li1,2, H. Lü1,3 and Liang Ma1
1 Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, 135 Yaguan Road, Tianjin 300350, China.
2 Department of Physics, McGill University, 3600 Rue University, Montreal, QC Canada.
3 Peng Huanwu Center for Fundamental Theory, Hefei, Anhui 230026, China.
* liyuezhou@physics.mcgill.ca, mrhonglu@gmail.com, liangma@tju.edu.cn
Abstract
It is known that the (a, c) central charges in four-dimensional CFTs are linear combinations of the three independent OPE coefficients of the stress-tensor three-point function. In this paper, we adopt the holographic approach using AdS gravity as an effect field theory and consider higher-order corrections up to and including the cubic Riemann tensor invariants. We derive the holographic central charges and OPE coefficients and show that they are invariant under the metric field redefinition. We further discover a hidden relation among the OPE coefficients that two of them can be expressed in terms of the third using differential operators, which are the unit radial vector and the Laplacian of a four-dimensional hyperbolic space whose radial variable is an appropriate length parameter that is invariant under the field redefinition. Furthermore, we prove that the consequential relation c = 1/3ℓeff ∂a/∂ℓeff and its higher-dimensional generalization are valid for massless AdS gravity constructed from the most general Riemann tensor invariants.
