General Axisymmetric Solutions and Self-Tuning in 6D Chiral Gauged Supergravity

TL;DR

This paper re-examines axially-symmetric solutions in 6D chiral gauged supergravity, clarifying the nature of singularities and brane tensions, and discusses implications for self-tuning mechanisms addressing vacuum energy.

Contribution

It identifies the subset of solutions with conical singularities that match previous results and clarifies the conditions under which brane tensions can be positive or negative.

Findings

Conical singularities correspond to specific solutions aligning with previous work.

Brane tensions can be positive or negative depending on parameters.

Non-conical solutions have distinct physical interpretations related to self-tuning.

Abstract

We re-examine the properties of the axially-symmetric solutions to chiral gauged 6D supergravity, recently found in refs. hep-th/0307238 and hep-th/0308064. Ref. hep-th/0307238 finds the most general solutions having two singularities which are maximally-symmetric in the large 4 dimensions and which are axially-symmetric in the internal dimensions. We show that not all of these solutions have purely conical singularities at the brane positions, and that not all singularities can be interpreted as being the bulk geometry sourced by neutral 3-branes. The subset of solutions for which the metric singularities are conical precisely agree with the solutions of ref. hep-th/0308064. Establishing this connection between the solutions of these two references resolves a minor conflict concerning whether or not the tensions of the resulting branes must be negative. The tensions can be both negative and positive depending on the choice of parameters. We discuss the physical interpretation of the non-conical solutions, including their significance for the proposal for using 6-dimensional self-tuning to understand the small size of the observed vacuum energy. In passing we briefly comment on a recent paper by Garriga and Porrati which criticizes the realization of self-tuning in 6D supergravity.