Hole Superconductivity in $Mg B_2$: a high $T_c$ cuprate without Cu

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 highly negatively charged $Cu-O$ 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 in the negatively charged $B^-$ planes. 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.