The Emergence of Localized Gravity

TL;DR

The paper investigates how four-dimensional gravity can emerge on a sub-critical brane in AdS5, as in the Karch–Randall scenario. It recasts graviton fluctuations into a Schrödinger-like problem and uses a solvable toy model to illuminate the localization mechanism, supported by numerical shooting that quantifies the bound-state mass and its dominance on the brane. A tower of Kaluza–Klein gravitons provides small corrections to AdS4 gravity, with the bound state governing long-distance behavior. The work also links localized gravity to AdS/CFT and boundary CFT considerations, offering a framework for how conformal symmetry and TT correlator effects could influence graviton masses and bridge holography with brane-localized gravity.

Abstract

We explore physics on the boundary of a Randall-Sundrum type model when the brane tension is slightly sub-critical. We calculate the masses of the Kaluza-Klein decomposition of the graviton and use a toy model to show how localized gravity emerges as the brane tension becomes critical. Finally, we discuss some aspects of the boundary conformal field theory and the AdS/CFT correspondence.

Figures (4)

• Figure 1: The energies $E$ of the first few eigenfunctions of the toy potential as a function of $\epsilon$. The emergence of the negative energy bound state can be seen as the brane tension is increased ($\epsilon \rightarrow 0$).
• Figure 2: Comparison of the toy model and exact wavefunction (solved numerically), for n=2 and $\epsilon = 0.01$. The value of the normalized wavefunctions are shown as a function of $w$. The brane is at $w=0$ and the boundary of $AdS_5$ at $w=\pi-\epsilon$.
• Figure 3: Mass of the bound state ($E_0$) as a function of $\epsilon$, calculated numerically.
• Figure 4: $E_0/\sin(\epsilon)$ (top) compared to $(1.5 - \epsilon)\sin\epsilon$ as a function of $\epsilon$.