A wife sulks and goes back to her parents' home without permission. Is she guilty of nushuz (marital defiance)?

Not necessarily — it depends on the reason and the duration; leaving out of fear, mistreatment or because no maintenance is given is not nushuz.
From the fiqh standpoint, a wife who leaves the house without permission and without a Shariah reason may be counted as guilty of nushuz. But before applying the label, the husband needs to ask: why did she leave? Often sulking is a sign of a hurt that has not been heard. The sunnah approach is to coax her gently, invite her home, and resolve the cause. Ali r.a. and Fatimah r.a. once had a disagreement, and the Prophet ﷺ coaxed Ali with an affectionate joke, "get up, O Abu Turab" (narrated by al-Bukhari). If it drags on, involve both families as arbiters (hakam). Determining nushuz for the purpose of maintenance is done by the Syariah Court. See Approaches to persuasion.