Interactive proofs for levels of the polynomial hierarchy We know that if you have a PSPACE machine, it's powerful enough to give an interactive proof of any level the polynomial hierarchy. (And if I remember right, all you need is #P.) But suppose you want to give an interactive proof of membership in a $\Sigma_2$ language. Is it enough to be able to solve problems in $\Sigma_2$? Is solving problems in $\Sigma_5$ adequate? More generally, if you can solve $\Sigma_k$ or $\Pi_k$ problems, for what $\Sigma_\ell$ is this sufficient to generate interactive proofs of all languates in $\Sigma_\ell$?

This question was inspired by this cstheory stackexchange question.
Even for giving an IP for coNP, using current techniques, one needs to arithmetize, i.e. use counting, which means essentially the full power of #P.  Any weaker prover even for coNP would be very interesting, I think (in particular would imply a new non relativing technique.)