Kicking the Rugby Ball: Perturbations of 6D Gauged Chiral Supergravity

TL;DR

This paper studies the stability of 6D chiral gauged supergravity compactifications with branes, finding marginal stability for conical geometries and positive mass modes otherwise, with explicit mode solutions for rugby-ball shapes.

Contribution

It provides a comprehensive analysis of scalar perturbations in warped 6D supergravity with branes, including explicit solutions and stability criteria, clarifying previous conflicting results.

Findings

Conical geometries are marginally stable for normalizable perturbations.

Nonconical geometries are stable for regular perturbations.

Explicit mode functions are derived for rugby-ball solutions.

Abstract

We analyze the axially-symmetric scalar perturbations of 6D chiral gauged supergravity compactified on the general warped geometries in the presence of two source branes. We find all of the conical geometries are marginally stable for normalizable perturbations (in disagreement with some recent calculations) and the nonconical for regular perturbations, even though none of them are supersymmetric (apart from the trivial Salam-Sezgin solution, for which there are no source branes). The marginal direction is the one whose presence is required by the classical scaling property of the field equations, and all other modes have positive squared mass. In the special case of the conical solutions, including (but not restricted to) the unwarped `rugby-ball' solutions, we find closed-form expressions for the mode functions in terms of Legendre and Hypergeometric functions. In so doing we show how to match the asymptotic near-brane form for the solution to the physics of the source branes, and thereby how to physically interpret perturbations which can be singular at the brane positions.