The p-zombie argument is the best-known of a group of conceivability arguments, which ultimately depend on the notion that if a proposition is conceivably true, then there is a metaphysically possible world in which it is true. Skeptics suppose that this is just a complicated way of equivocating over what 'conceivable' means, and even David Chalmers, the philosopher who has done the most to bring the p-zombie argument to wide attention, acknowledges that it depends on the assumption of what he calls 'perfect conceivability', which is tantamount to irrefutable knowledge.

To deal with the awkwardly apparent fact that consciousness certainly seems to have physical effects, zombiephiles challenge the notion that physics is causally closed, so that it is conceivable that something non-physical can cause physical effects. Their approach is to say that the causal closure of physics is not provable, but at this point, the argument has become a lexicographical one, about the definition of the words 'physics' and 'physical' (if one insists that 'physical' does not refer to a causally-closed concept, then we still need a word for the causal closure within which the physical is embedded - but that's just what a lot of people take 'physical' to mean in the first place.) None of the anti-physicalists have been able, so far, to shed any light on how the mind is causally effective in the physical world.

You might be interested in the late Daniel Dennett's "The Unimagined Preposterousness of Zombies": https://dl.tufts.edu/concern/pdfs/6m312182x