Complementarity of the Maldacena and Karch-Randall Pictures

TL;DR

The paper tests the AdS/CFT-based complementarity of the Karch-Randall braneworld by performing a one-loop calculation of the graviton self-energy on an $AdS_4$ brane in $AdS_5$. By decomposing the self-energy into transverse-traceless and trace parts, it shows that a constant piece generates a graviton mass while preserving diffeomorphism invariance, with the mass matching the Karch-Randall prediction in the appropriate limit. The calculation aggregates scalar, fermion, and vector contributions from an ${\cal N}=4$ super-Yang–Mills multiplet, finding a universal spin-structure ratio $1:3:12$ tied to the Weyl anomaly. The result reinforces the holographic view that quantum CFT effects on the brane dynamically realize a massive graviton, with the coefficient $\alpha$ playing a central, universal role across Minkowski and AdS braneworlds.

Abstract

We perform a one-loop test of the holographic interpretation of the Karch-Randall model, whereby a massive graviton appears on an AdS_4 brane in an AdS_5 bulk. Within the AdS/CFT framework, we examine the quantum corrections to the graviton propagator on the brane, and demonstrate that they induce a graviton mass in exact agreement with the Karch-Randall result. Interestingly enough, at one loop order, the spin 0, spin 1/2 and spin 1 loops contribute to the dynamically generated (mass)^2 in the same 1: 3: 12 ratio as enters the Weyl anomaly and the 1/r^3 corrections to the Newtonian gravitational potential.