We argue that global charges, such as baryon or lepton number, are not conserved in theories with the Standard Model fields localized on the brane which propagates in higher-dimensional space-time. The global-charge non-conservation is due to quantum fluctuations of the brane surface. These fluctuations create "baby branes" that can capture some global charges and carry them away into the bulk of higher-dimensional space. Such processes are exponentially suppressed at low-energies, but can be significant at high enough temperatures or energies. These effects can lead to a new, intrinsically high-dimensional mechanism of baryogenesis. Baryon asymmetry might be produced due either to "evaporation" into the baby branes, or creation of the baryon number excess in collisions of two Brane Universes. As an example we discuss a possible cosmological scenario within the recently proposed "Brane Inflation" framework. Inflation is driven by displaced branes which slowly fall on top of each other. When the branes collide inflation stops and the Brane Universe reheats. During this non-equilibrium collision baryon number can be transported from one brane to another one. This results in the baryon number excess in our Universe which exactly equals to the hidden "baryon number" deficit in the other Brane Universe.
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