Locally Localized Gravity

TL;DR

The paper shows that four-dimensional gravity can be localized on an AdS$_4$ brane embedded in AdS$_5$ even when the would-be zero-mode is non-normalizable, by a very light massive bound graviton state. It formulates the problem as a TT fluctuation spectrum mapped to a one-dimensional Schrödinger equation with volcano-type potentials, revealing a discrete spectrum with an almost-zero mode and a heavy KK tower. The analysis distinguishes between dS$_4$ and AdS$_4$ cases, finding a massless bound state for dS$_4$ but not for AdS$_4$, while still obtaining effective 4D gravity on the brane through localization. The work highlights the locality of gravity localization, discusses brane bending and radion-like modes, and hints at holographic interpretations involving the AdS$_5$ boundary and a boundary disk, with implications for string theory realizations and no-go theorems. Overall, it demonstrates that localized gravity is achievable without a normalizable zero mode, broadening the landscape of braneworld phenomenology and holography.

Abstract

We study the fluctuation spectrum of linearized gravity around non-fine-tuned branes. We focus on the case of an AdS4 brane in AdS5. In this case, for small cosmological constant, the warp factor near the brane is essentially that of a Minkowski brane. However, far from the brane, the metric differs substantially. The space includes the AdS5 boundary, so it has infinite volume. Nonetheless, for sufficiently small AdS4 cosmological constant, there is a bound state graviton in the theory, and four-dimensional gravity is reproduced. However, it is a massive bound state that plays the role of the four-dimensional graviton.

Figures (11)

• Figure 1: The behavior of the warp-factor for $\Lambda=-1$, 0 and 1.
• Figure 2: The Minkowski volcano potential.
• Figure 3: The deSitter volcano potential.
• Figure 4: The Anti-deSitter volcano potential.
• Figure 5: Schematics of the Penrose diagrams of the dS and Minkowski. The spacetime one is instructed to keep is shaded. Since the branes are accelerated, they have their own horizon, only for the Minkowski brane does this coincide with the Poincare patch horizon. The spacetime one wants to keep is between the brane and the horizon. The dS brane really is a full hyperboloid, the part drawn corresponding to the static slice of dS. In the case of the AdS brane the brane falls through the horizon of the Poincare patch. It is more useful to study the embedding in terms of an constant time slice through global AdS.