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[Warhammer 40K] Would a Null Field kill a psyker?

From what I understand, Null Fields remove the ability to connect to the Warp from an area. If a psyker was within its bounds, would they be cut off from the Warp and die?

Going off of that, if the Cadian Pylons are a kind of souped up Null Field generator that helps keep the Eye of Terror in check, then can Psykers even work on Cadia and the surrounding area?
gpt
No, Null fields simply limits the connection Pyskers have, if it severed it completely all people with souls (the connection to the Warp) would just roll over and die.

Psykers can still use psykic power, it's just very limited (this can depend on the quality and strength of the field generator).  
A low level psyker? Can't do shit in a Null Field, A high ranked powerful Chaos Sorcerer? Lost the ability to cast some of the more powerful spells.

About the Cadian Pylons, we don't know anything about them. All we know is that they keep the Cadian gate up, we don't even know if they are Null Fields Generators.