Comparative law notes
In the context of German stock corporation law, the term Aufsichtsrat has a very specific meaning and purpose. It is far narrower than the classic definition given here in English. However, the universally accepted and most frequently used translation of that German term is indeed "supervisory board". When a text discusses Aufsichtsrat as a general concept independently of any specific company, the English phrase should be in lower case. When the text is discussing a specific company and its Aufsichtsrat, the writer may choose to capitalize that term to serve as a kind of proper noun.