nLab list of functorial field theories

This article is meant to give an exhaustive list of explicitly constructed nontopological functorial field theories in dimension 2 and higher. All currently known explicit constructions are nonextended, and with the exception of the Kandel construction, have dimension 2.

Free field theories

Massless boson

Massive boson

  • Santosh Kandel?, Functorial Quantum Field Theory in the Riemannian setting, arXiv.


  • James E. Tener?, Construction of the unitary free fermion Segal CFT, arXiv.

Field theories with interaction


  • Doug Pickrell?, P(phi)2 quantum field theories and Segal’s axioms_, arXiv.
S(Φ)= Σ2 1(dΦ 2+m 2Φ 2)+P(Φ)S(\Phi)=\int_\Sigma 2^{-1}(\|d\Phi\|^2+m^2\Phi^2)+P(\Phi)

Liouville field theory

See Liouville theory for more information.

  • Colin Guillarmou, Antti Kupiainen, Rémi Rhodes, Vincent Vargas, Segal’s axioms and bootstrap for Liouville Theory, arXiv.

Last revised on May 8, 2024 at 02:40:27. See the history of this page for a list of all contributions to it.