Will a man who commits adultery with a married woman, or touches her, or looks at her, be subjected to retribution by her husband on the Day of Judgment, and what is the expiation for this sin?

Adultery is a grave sin and a great iniquity. If a man commits adultery with a married woman, his sin is multiplied. He must offer sincere repentance to Allah Almighty. It is not a condition for the validity of repentance to inform the woman's husband or seek his forgiveness, due to the harm that would cause the woman and the door to mischief it would open. It is sufficient for him to repent sincerely to Allah and seek His forgiveness. There is no specific expiation required other than repentance.