There is no lawsuit for adultery in your state--very few states still let a spouse sue over adultery. What the wife is doing is bringing up his adultery in family court as grounds to get sole custody of their children, which she can do: family court can decide child custody based on the home environment, the parents' respective associates and actions, and the children's best interest. Your boyfriend can bring up her adultery in return as a factor to be considered for child custody. Adultery may also affect other aspects of divorce. But there is no separate lawsuit for adultery in GA.