PCT Theorem, Wightman Axioms and Conformal Bootstrap

TL;DR

This paper uses the Wightman axiomatic framework to derive conformal bootstrap equations for four-point functions, emphasizing the role of PCT symmetry and weak local commutativity in conformal field theory.

Contribution

It adapts the Wightman axioms to conformal field theory to derive bootstrap equations, highlighting the connection between PCT theorem and weak local commutativity.

Findings

Derived conformal bootstrap equations from Wightman axioms.

Demonstrated the analytic continuation relationship between two Wightman functions.

Highlighted the role of PCT symmetry in conformal field theory.

Abstract

The axiomatic Wightman formulation for nonderivative conformal field theory is adopted to derive conformal bootstrap equation for the four point function. The equivalence between PCT theorem and {\it weak local commutativity}, due to Jost, play a very crucial role in axiomatic field theory. The theorem is suitably adopted for conformal field theory to derive the desired equations in CFT. We demonstrate that the two Wightman functions are analytic continuation of each other.