Which Languages Have 4-Round Zero-Knowledge Proofs?

We show that if a language L has a 4-round, black-box, computational zero-knowledge proof system with negligible soundness error, then \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\bar{L}\in \mathsf{MA}$\end{document}. Assuming the polynomial hierarchy does not collapse, this means in particular that NP-complete languages do not have 4-round zero-knowledge proofs with black-box simulation.