Here's the New York Times answer:

This is between you and your spouse. You should tell her you want to separate, just as you would if she were sleeping with the mailman. The idea of “suffering in silence” for the good of the project is illogical. How would the quiet divorce of this man’s mistress hurt an international leadership initiative? He’d probably be relieved.
[...]
Do you admire this man so much that you haven’t asked your wife why she keeps having sex with him? I halfway suspect you’re writing this letter because you want specific people to read this column and deduce who is involved and what’s really going on behind closed doors (without actually addressing the conflict in person). That’s not ethical, either.