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.Comment: 27 pages, 1 figure; JHEP3 style; Some references added, and
discussion of tension constraints and unwarped solutions made more explici