Grounds for an ethics complaint? UK math prof. publicly misrepresenting results from an unrelated discipline
First, and foremost, be very cautious about taking this issue outside of the scientific realm of argument.  If you start to file ethics charges or libel lawsuits, then you are likely to be casting yourself in the role of censorious scientific villain, and it is likely to not go well for you.

Instead, if you feel that your work really is scientifically defensible, I recommend that you stick entirely to the evidence to defend it.  If you cannot do so, then that is a serious problem --- having not read your thesis, I have no idea whether you or your critic has a better case.  Do note, however, that being in a different discipline does not immunize you from a person's criticism: a critic need not have any credential at all to point out a potential flaw in your work, and the nature of science is that if you cannot defend against criticism, your work cannot stand.

Finally, I would strongly recommend talking to your advisor before you take any further steps and strongly heeding their advice.  Your advisor is likely to know better than you whether to take your critic seriously, given the state of your work and the field, as well as what types of response are likely to be wise or foolish.