Calculus of Variations and Geometric Measure Theory

G. B. De Luca - N. De Ponti - A. Mondino - A. Tomasiello

Harmonic functions and gravity localization

created by mondino on 12 Jun 2023
modified on 23 Aug 2023


Accepted Paper

Inserted: 12 jun 2023
Last Updated: 23 aug 2023

Journal: The Journal of High Energy Physics
Year: 2023

ArXiv: 2306.05456 PDF


In models with extra dimensions, matter particles can be easily localized to a `brane world', but gravitational attraction tends to spread out in the extra dimensions unless they are small. Strong warping gradients can help localize gravity closer to the brane.

In this note we give a mathematically rigorous proof that the internal wave-function of the massless graviton is constant as an eigenfunction of the weighted Laplacian, and hence is a power of the warping as a bound state in an analogue Schr\"odinger potential. This holds even in presence of singularities induced by thin branes.

We also reassess the status of AdS vacuum solutions where the graviton is massive. We prove a bound on scale separation for such models, as an application of our recent results on KK masses. We also use them to estimate the scale at which gravity is localized, without having to compute the spectrum explicitly. For example, we point out that localization can be obtained at least up to the cosmological scale in string\$M$-theory solutions with infinite-volume Riemann surfaces; and in a known class of ${\mathcal N}=4$ models, when the number of NS5- and D5-branes is roughly equal.