  The nature of the effective interaction responsible for pairing in the
high-temperature superconducting cuprates remains unsettled. This question has
been studied extensively using the simplified single-band Hubbard model, which
does not explicitly consider the orbital degrees of freedom of the relevant
CuO$_2$ planes. Here, we use a dynamic cluster quantum Monte Carlo
approximation to study the orbital structure of the pairing interaction in the
three-band Hubbard model, which treats the orbital degrees of freedom
explicitly. We find that the interaction predominately acts between neighboring
copper orbitals, but with significant additional weight appearing on the
surrounding bonding molecular oxygen orbitals. By explicitly comparing these
results to those from the simpler single-band Hubbard model, our study provides
strong support for the single-band framework for describing superconductivity
in the cuprates.
