CFT Osterwalder-Schrader Theorem

Most QFT axioms are only good to prove theorems but not to compute anything measurable. One exception are the Euclidean Conformal Field Theory (CFT) axioms in d>=3 dimensions, which do lead to surprisingly strong “bootstrap" constraints on scaling dimensions of various conjecturally existing Euclidean CFTs (such as the critical point of the 3d Ising and O(2) models). In this talk I will not discuss the bootstrap as such, but I will explain the Euclidean CFT axioms and will relate them to the Osterwalder-Schrader and Wightman axioms. The OS linear growth condition does not obviously follow from the Euclidean CFT axioms, but fortunately there is a route to Wightman axioms which does not rely on the Glaser-Osterwalder-Schrader construction. Based on work in progress with Petr Kravchuk and Jiaxin Qiao.

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