Legal Question in Employment Law in Georgia

Absent a contract, there is no general right or entitlement to a job and employees can be terminated for any or no reason (except very few discriminatory reasons not raised in your post). Given that, based only on your post, you don't raise a legal issue with the employer. You might have a claim for slander against another person who makes false accusations against you, if that is the case, but whether it is worth the time and trouble is another question. I note that nowhere in your post do you say the accusations were not true - you just state that you don't think they have proof.