Abstract
The (m2,Lambda) plane of spin s>1 massive fields in (anti-) de Sitter space backgrounds is shown to consist of separate phases, divided by lines of novel "partially massless" gauge theories that successively remove helicities, starting from the lowest, 0 or +/-1/2. The norms of the excluded states flip as the gauge lines are crossed and only the region containing the massive Minkowski theory is unitary. The partially massless gauge theories are unitary or not, depending on the ordering of the gauge lines. This "level splitting" of massless Minkowski gauge theories is specific to nonzero Lambda.
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