Algebraic conformal quantum field theory in perspective
Karl-Henning Rehren
TL;DR
This paper reviews algebraic conformal quantum field theory, emphasizing its rigorous constructions and classifications in two dimensions, and discusses potential applications of these insights to four-dimensional quantum field theory.
Contribution
It provides a comprehensive perspective on algebraic conformal QFT, highlighting recent developments, classifications, and the potential for extending methods to higher dimensions.
Findings
Rigorous constructions in two-dimensional conformal QFT
Complete classifications of models in two dimensions
Potential applications of algebraic methods to four-dimensional QFT
Abstract
Conformal quantum field theory is reviewed in the perspective of Axiomatic, notably Algebraic QFT. This theory is particularly developped in two spacetime dimensions, where many rigorous constructions are possible, as well as some complete classifications. The structural insights, analytical methods and constructive tools are expected to be useful also for four-dimensional QFT.
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