Emotional abuse can be intimidation, threats, emotional blackmail, coercion, criticism, pressure, punishments for breaking an arbitrary set of rules (e.g., prolonged silent treatment, withholding affection, etc), gaslighting, lying to make themselves seem better and you by comparison seem worse, and more besides.
There are many people who don't like to apply the term 'emotional abuse' to their relationship as it seems really drastic, abuse is such a heavy word. But if your partner’s behaviour makes you feel like less of a person than you actually are, makes you feel like you're being controlled or like you can't talk about what’s wrong with the relationship without being immediately shut down, makes you doubt yourself, it’s abusive. If your partner is stopping you from being able to express yourself in any way, it’s abusive. If you feel you have to modify your behaviour to accommodate your partner’s behaviour or modify your behaviour to avoid negative consequences from your partner, it’s abusive.
What do you mean by lying about having an affair? The details of the situation aren't clear from your OP but persistently lying about something as a means of control over another person would be abuse.