Is it still possible to sue Ex for defamation of character/ slander?

A few months ago I was informed that there is a warrant issued for me in another state. Apparently my ex pressed charges for something that never happened when she found out I was with someone else. The warrant is from 2009 and is a misdemeanor which means I or her would have to physically go into the courthouse to resolve anything. Which means I would have to miss work and possibly be arrested for something I didn't do. My question is how can I Sue my ex for all the lies and slander on my name? This warrant is following me every where, causing me and my family stress and giving my ex something to hold over my head. Do I Sue her or the state?? There's no way either one has any proof for something that never happened.