Categoria:
Altro (categoria non censita)
Categoria non censita:
Operator Algebra Seminar
Data e ora inizio evento:
Data e ora fine evento:
Aula:
Altro (Aula esterna al Dipartimento)
Sede:
Dipartimento di Matematica, Università di Roma Tor Vergata
Aula esterna:
Aula Dal Passo
Speaker:
Tiziano Gaudio
In the recent work arXiv:2303.17190v2, G. Höhn and S. Möller propose a classification of vertex operator superalgebras (VOSAs) with central charge at most 24 and with trivial representation theory. VOSAs with the latter property are usually called self-dual or holomorphic. From the point of view of the operator algebraic approach to chiral Conformal Field Theory, it is a natural question whether they give rise to graded-local conformal nets of von Neumann algebras. Indeed, this happens if one proves that those VOSAs are unitary and they satisfy the strong graded locality condition, according to the correspondence given by Carpi, Gaudio and Hillier, which extends to the Fermi case the one by Carpi, Kawahigashi, Longo and Weiner of 2018. In this seminar, based on the work arXiv:2410.07099v2, we discuss the unitarity of holomorphic VOSAs with central charge at most 24. To do that we need to recall the notion of complete unitarity for vertex operator algebras and the recent developments regarding their extensions. Then we move to their strong graded locality, which is established for most of them. Indeed, this property remains an open problem for only 59 out of 969 VOSAs in the central charge 24. Nevertheless, we obtain many new examples of holomorphic graded-local conformal nets. They can be considered as the Fermi counterparts of the models recently built from the so-called Schellekens list. The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/home-page?authuser=0
Contatti/Organizzatori:
morinell@mat.uniroma2.it