On massless 4D Gravitons from 5D Asymptotically AdS Space-times
Elias Kiritsis, Francesco Nitti
TL;DR
This work analyzes 5D Einstein–Dilaton geometries that are asymptotically AdS$_5$ and seeks a normalizable massless 4D graviton in the spectrum of fluctuations. Using a linearized fluctuation analysis, the tensor sector reduces to a Schrödinger problem with potential $V_t=B'^2-B''$, where $B(y)=-\tfrac{3}{2}\log a(y)$ encodes the warp factor, and normalizability dictates whether a 4D graviton can emerge. The central result is that such a massless spin-2 mode can exist only if the extra dimension ends at finite $y_0$ via an IR boundary or a singularity; in the latter case, a massless graviton can appear as the sole low-energy degree of freedom provided appropriate boundary conditions at the singularity are chosen, though these conditions are not universal and depend on the IR physics. The study connects holographic interpretations to IR dynamics of a dual 4D theory and discusses implications for no-go theorems and possible generalizations, including massive gravitons or altered boundary assumptions.
Abstract
We investigate the conditions for obtaining four-dimensional massless spin-2 states in the spectrum of fluctuations around an asymptotically $AdS_5$ solution of Einstein-Dilaton gravity. We find it is only possible to have normalizable massless spin-2 modes if the space-time terminates at some IR point in the extra dimension, far from the UV AdS boundary, and if suitable boundary conditions are imposed at the ``end of space.'' In some of these cases the 4D spectrum consists only of a massless spin-2 graviton, with no additional massless or light scalar or vector modes. These spin-2 modes have a profile wave-function peaked in the interior of the 5D bulk space-time. Under the holographic duality, they may be sometimes interpreted as arising purely from the IR dynamics of a strongly coupled QFT living on the AdS boundary.