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

We re-examine the properties of the axially-symmetric solutions to chiralgauged 6D supergravity, recently found in refs. hep-th/0307238 andhep-th/0308064. Ref. hep-th/0307238 finds the most general solutions having twosingularities which are maximally-symmetric in the large 4 dimensions and whichare axially-symmetric in the internal dimensions. We show that not all of thesesolutions have purely conical singularities at the brane positions, and thatnot all singularities can be interpreted as being the bulk geometry sourced byneutral 3-branes. The subset of solutions for which the metric singularitiesare conical precisely agree with the solutions of ref. hep-th/0308064.Establishing this connection between the solutions of these two referencesresolves a minor conflict concerning whether or not the tensions of theresulting branes must be negative. The tensions can be both negative andpositive depending on the choice of parameters. We discuss the physicalinterpretation of the non-conical solutions, including their significance forthe proposal for using 6-dimensional self-tuning to understand the small sizeof the observed vacuum energy. In passing we briefly comment on a recent paperby Garriga and Porrati which criticizes the realization of self-tuning in 6Dsupergravity.Comment: 27 pages, 1 figure; JHEP3 style; Some references added, and discussion of tension constraints and unwarped solutions made more explici