Operator algebras and vertex operator algebras

Sebastiano Carpi
March 22, 2016
In two-dimensional conformal field theory (CFT) the building blocks are given by chiral CFTs, i.e.~CFTs on the unit circle (compactified light-ray). They are generated by quantum fields depending on one light-ray coordinate only. There are two mathematical formulations of chiral CFT, the one based on vertex operator algebras (VOAs) and the one based on conformal nets. We describe some recent results which, for first time, gives a general construction of conformal nets from (unitary) VOAs.
open access link The Fourteenth Marcel Grossmann Meeting, World Scientific, 2017
@inproceedings{Carpi:2016tog, author = "Carpi, Sebastiano", title = "{Operator algebras and vertex operator algebras}", booktitle = "{Proceedings, 14th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics, and Relativistic Field Theories (MG14) (In 4 Volumes): Rome, Italy, July 12-18, 2015}", year = "2017", volume = "4", pages = "3843-3848", doi = "10.1142/9789813226609_0508", eprint = "1603.06742", archivePrefix = "arXiv", primaryClass = "math.OA", SLACcitation = "%%CITATION = ARXIV:1603.06742;%%" }