Erlangen 2026 – wissenschaftliches Programm

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 3: Quantum Field Theory I: Axiomatic, Probabilistic, Algebraic, Conformal

MP 3.1: Hauptvortrag

Dienstag, 17. März 2026, 16:15–16:45, KH 02.013

Osterwalder-Schrader axioms for a class of unitary 2D Conformal Field Theories — •Maria Stella Adamo¹, Yuto Moriwaki², and Yoh Tanimoto³ — ¹Department Mathematik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstrasse 11, 91058 Erlangen, Germany — ²Interdisciplinary Theoretical and Mathematical Science Program (iTHEMS) Wako, Saitama 351-0198, Japan — ³Dipartimento di Matematica, Università di Roma "Tor Vergata", Via della Ricerca Scientifica 1, I-00133 Roma, Italy

We provide a brief overview of axiomatic frameworks for quantum field theory in the case where the spacetime is 2-dimensional and the theory is invariant under conformal transformations, with a particular focus on the Wightman formalism of quantum fields.

For a general quantum field theory, the reconstruction theorem by Osterwalder-Schrader provides conditions to be verified by correlation functions in the Euclidean space to produce a quantum field theory in the Wightman formalism. In our work, for a reasonable class of unitary full Vertex Operator Algebras describing a class of unitary 2D conformal field theories, we construct Euclidean correlation functions that verify a conformal version of the Osterwalder-Schrader axioms.

Keywords: Conformal Field Theory; Wightman formalism; Vertex Operator Algebras; Osterwalder-Schrader reconstruction