Solving the hierarchy problem with brane crystals

The brane world scenario advocated by Arkani-Hamed et al. transmutes the hierarchy problem into explaining why extra dimensions have sizes much larger than the fundamental scale. In this Letter we discuss possible solutions to this problem by considering the compactified dimensions to be populated by a large number of branes in a crystal lattice. The experimental consequences of this scenario are described, including the presence of large energy gaps in the spectrum of Kaluza–Klein modes.