The theory of hole superconductivity explains high temperature superconductivity in cuprates as driven
by pairing of hole carriers in oxygen $p\pi$ orbitals in the $Cu-O$ planes. The pairing mechanism is
hole undressing and is Coulomb-interaction driven. We propose that the planes of B atoms in $Mg
B_2$ are akin to the $Cu-O$ planes without Cu, and that the recently observed high temperature
superconductivity in $Mg B_2$ arises similarly from undressing of hole carriers in the planar boron
$p_{x,y}$ orbitals. Doping $Mg B_2$ with electrons and with holes should mirror the behavior of
underdoped and overdoped high $T_c$ cuprates respectively. We discuss possible ways to achieve
higher transition temperatures in boron compounds based on this theory.
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