Conformally Invariant Gauge Theory of 3-Branes in 6D and the Cosmological Constant

It is shown that the gauge theory of relativistic 3-Branes can be formulated in a conformally invariant way if the embedding space is six-dimensional. The implementation of conformal invariance requires the use of a modified measure, independent of the metric in the action. Brane-world scenarios without the need of a cosmological constant in 6D are constructed. Thus, no ``old'' cosmological constant problem appears at this level.