I have a question that pertains particularly to the Eldar's Swooping Hawks and Fire Prism combat cards, but it is generally applicable to situations where a player is forced to lose combat tokens. My question is, if the player has no tokens of the appropriate type but he or she has dice of that type, does the player receive "negative" tokens and receive a penalty to the icon total for the turn, or is the benefit lost.

For instance, the Fire Prism can be used to reduce the opponent's shield tokens by five if used by a defending player with unrouted Falcons or Void Stalkers. If I use this against an opponent with no shield TOKENS but a total of six shield DICE and CARD ICONS, does this bring him down to one shield for the round it is played, or is this effect wasted?

If one is to be exact about the wording, it seems like it would be wasted, because you're supposed to lose tokens, and you don't have them. But I can understand if this was not the intended interpretation. I'm surprised that I haven't run across this elsewhere as a question or clarification.

If, at that time, the opponent does not already have the specified tokens, then nothing happens.

On the combat cards they make a distinct difference between tokens (symbol in circle) and dice (symbol in square).
If your combat card says your opponent looses shield tokens then that's exactly what they mean. If your opponent does not have any tokens he cannot loose any.

Thanks guys...that seemed like the right interpretation from my literal reading. The only thing that made me question it was the Fire Prism card seems to be extremely situational; in practice, I don't know if I've ever seen a player with five shield tokens in a single round.

I agree, it is situational. It is a go to for Advanced Space Marines or a defense focused Chaos, but it can be a bit inefficient in general use.

The 5 shield removal speaks to me more of how powerful the effect is, not about how efficient it is meant to be.

There is one situation that I can think of where an opponent would have 5 or more defence tokens. That is using the Adeptus Mechanicus event card as space marines while in possession of 3 forge tokens. Rare but it could happen!