Answer:
   
   In theory, if a wife has an affair the husband is obligated to get
   divorced. Again...in theory. In practice, we do not require the court
   to believe the evidence. However, in such a situation, lamentably,
   there is often no marriage to try to save. The wife left. The man
   ought to give her a get, a divorce writ. These can really only be
   handled by a beis din, a religious court.
   
   Note: Since a decree by Rabbeinu Gershom in the 10th century, a man
   not only must give the writ, the wife must willingly accept it. If she
   does not, the marriage is not terminated. In which case, things can
   get pretty difficult. There are ways to deal with this situation, but
   again, it really requires a beis din.