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It all does depend on the severity of the accusations and if it amounts to defamation of character and/or having an adverse effect on your life. So example, if they are spreading rumours and lies about you or posting untrue things up on social media etc and it is having an ill effect on you then yes, you may report them to the authorities and sue them.
My advice at present is to keep a record and document all things which have been said about you just incase you need to take further action.
I hope I have assisted. Please take a moment to provide a positive rating. Thank you. John.