Stability and Fluctuations on Walls in N=1 Supergravity

TL;DR

This paper analyzes non-BPS multi-wall configurations in N=1 supergravity, showing they lack tachyonic fluctuations, and explores the properties of localized gravitons, gravitinos, and the radion mass in relation to the model's parameters.

Contribution

It demonstrates the stability of non-BPS multi-wall configurations and derives the radion mass dependence, providing insights into localized supermultiplets and boundary conditions.

Findings

Radion mass is exponentially suppressed by wall width and compactification radius.

Localized massless graviton and gravitino form a supermultiplet.

No tachyonic scalar fluctuations in the configurations.

Abstract

The recently found non-BPS multi-wall configurations in the N=1 supergravity in four dimensions is shown to have no tachyonic scalar fluctuations without additional stabilization mechanisms. Mass of radion (lightest massive fluctuation) is found to be proportional to $Lambda {\rm e}^{-\pi\Lambda R/2}$, where $\Lambda $ is the inverse width of the wall and $ R$ is the radius of compactified dimension. We obtain localized massless graviton and gravitino forming a supermultiplet with respect to the Killing spinor. The relation between the bulk energy density and the boundary energy density (cosmological constants) is an automatic consequence of the field equation and Einstein equation. In the limit of vanishing gravitational coupling, the Nambu-Goldstone modes are reproduced.