The Bros-Iagolnitzer analysis of analytic singularities in QFT can be generalised to analytic curved spacetimes. This leads naturally to the notion of the analytic microsupport. I will give some physics intuition that motivates the introduction of analytic states and will show that one can prove the timelike tube theorem in quantum field theory on curved spacetimes under plausible assumptions on the microsupport of the n-point functions.
(Joint work with E. Witten)