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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

Conformally invariant gauge theory of 3-branes in 6D and the cosmological constant