Hidden relations of central charges and OPEs in holographic CFT

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 = 1/3l(eff)partial derivative a/partial derivative l(eff )and its higher-dimensional generalization are valid for massless AdS gravity constructed from the most general Riemann tensor invariants.

Automated summary

In this paper, the holographic central charges and OPE coefficients in four-dimensional CFTs are derived using AdS gravity as an effective field theory, with a focus on their invariance under metric field redefinition and a hidden relation among the OPE coefficients. Furthermore, it is proven that a specific relation holds for massless AdS gravity constructed from the most general Riemann tensor invariants, demonstrating the consistency of the derived results.