Higher structures in Lorentzian quantum field theory

par Marco Benini (Genua)

vendredi 13 févr. 2026, 14:00 → 15:00 Europe/Paris

Fokko du Cloux (Bat. Braconnier)

One of the mathematical challenges posed by quantum field theory (QFT) is the quest for its axiomatization. This quest becomes even more challenging when the higher structures emerging from gauge theories are taken into account. In Lorentzian signature, two prominent axiomatizations are based on algebraic QFTs and factorization algebras, respectively. In the 1-categorical setting, thus ignoring the higher structures coming from gauge theories, these two candidates are equivalent as a consequence of the so-called time-slice axiom, which captures well-posedness of the underlying Cauchy problem. Unfortunately, the higher categorical analog of this equivalence turns out to be quite elusive. After reviewing the 1-categorical equivalence, I shall propose a new approach towards establishing its higher categorical analog, which crucially relies on a homotopically relaxed version of the time-slice axiom. Such higher categorical equivalence would entail that Lorentzian QFTs, including the higher structures coming from gauge theories, can be axiomatized equivalently by algebraic QFTs and by (time-orderable pre)factorization algebras.