beyondRCFT

I led as PI the project "Beyond Rationality in Algebraic CFT: mathematical structures and models", acronym: beyondRCFT, period: September 2019 - August 2022.

The project has been funded as a Marie Skłodowska–Curie Individual Fellowship (Global Fellowship) by the European Union's Horizon 2020 research and innovation programme H2020-MSCA-IF-2017 under Grant Agreement n. 795151 (CORDIS EU funding page beyondRCFT, DOI: 10.3030/795151, in H2020 MSCA, see also HORIZON MSCA). Coordinator: University of Rome Tor Vergata. Partner institution: Vanderbilt University.

This allowed me to spend the initial Outgoing phase of the project (September 2019 - August 2021) in the US at Vanderbilt University, Department of Mathematics, Nashville, Tennessee, with supervisor Dietmar Bisch, and the Return phase (September 2021 - August 2022) in Italy at the University of Rome Tor Vergata, Department of Mathematics, with supervisor Roberto Longo.

Project's abstract

Conformal Field Theory (CFT) in low dimensions is one of the most active branches of modern physics, it is amenable to rigorous "axiomatic" formulations, hence it is naturally connected to various areas of mathematical research. For example, to CFTs one can associate braided tensor categories (describing superselection sectors, defects, topological field theories) and subfactors, i.e. inclusions of von Neumann algebras with trivial center (describing extensions, duality properties and exotic charge localizations). All these areas are independently pairwise correlated, e.g. subfactors with CFTs, subfactors with tensor categories, and they have their own history and an extremely profound literature.

The aim of my research project is to analyze models of CFT, together with the associated mathematical objects, which are not necessarily "rational", i.e. which may admit infinitely many superselection sectors ("particle" excitations of the vacuum). Examples of non-rational CFTs (which are the majority among all CFTs) come from Virasoro minimal models with central charge bigger than one (there are continuously many), and global gauge theories with respect to a compact non-finite group of internal symmetries.

Non-rationality of a CFT also implies that the "size" of the associated categories and subfactors have to be infinite, namely one is led to consider categories with infinite spectrum and subfactors with infinite Jones index. These mathematical objects are natural generalizations of their "finite" counterparts (modular and fusion categories, finite index subfactors), they are physically motivated, but they attracted the attention of researchers only in recent times.

This research project aims to study structural properties of non-rational CFTs using modern machinery (e.g. generalized Q-systems, ind-categories, planar algebras), to study infinite braided tensor categories and infinite index subfactors arising from them, and exploit their interplay.

Resulting publications

L. Giorgetti. Quantum Operations in Algebraic QFT. Functional Analysis, Approximation Theory and Numerical Analysis, FAATNA20>22, Matera, Italy, 2022, conference proceedings. Note Mat., 43:41–56, 2023. (arXiv:2303.15171, DOI: 10.1285/i15900932v43n1p41)
M. S. Adamo, L. Giorgetti, Y. Tanimoto. Wightman fields for two-dimensional conformal field theories with pointed representation category. Comm. Math. Phys., 404:1231–1273, 2023. (arXiv:2301.12310, DOI: 10.1007/s00220-023-04835-1)
S. Carpi, T. Gaudio, L. Giorgetti, R. Hillier. Haploid algebras in C*-tensor categories and the Schellekens list. Comm. Math. Phys., 402:169–212, 2023. (arXiv:2211.12790, DOI: 10.1007/s00220-023-04722-9)
M. Bischoff, S. Del Vecchio, L. Giorgetti. Quantum operations on conformal nets. Rev. Math. Phys., 35:2350007-1–30, 2023. (arXiv:2204.14105, DOI: 10.1142/S0129055X23500071)
L. Giorgetti, A. J. Parzygnat, A. Ranallo, B. P. Russo. Bayesian inversion and the Tomita-Takesaki modular group. Quart. J. Math., 74:975–1014, 2023. (arXiv:2112.03129, DOI: 10.1093/qmath/haad014, available here)
L. Giorgetti. A planar algebraic description of conditional expectations. Internat. J. Math., 33:2250037-1–23, 2022. (arXiv:2111.04488, DOI: 10.1142/S0129167X22500379)
M. Benini, L. Giorgetti, A. Schenkel. A skeletal model for 2d conformal AQFTs. Comm. Math. Phys., 395:269–298, 2022. (arXiv:2111.01837, DOI: 10.1007/s00220-022-04428-4)
M. Bischoff, S. Del Vecchio, L. Giorgetti. Galois correspondence and Fourier analysis on local discrete subfactors. Ann. Henri Poincaré, 23:2979–3020, 2022. (arXiv:2107.09345, DOI: 10.1007/s00023-022-01154-4)
M. Bischoff, I. Charlesworth, S. Evington, L. Giorgetti, D. Penneys. Distortion for multifactor bimodules and representations of multifusion categories. arXiv:2010.01067, 2020.
L. Giorgetti, W. Yuan. Realization of rigid C*-bicategories as bimodules over type II1 von Neumann algebras. Adv. Math., 415:108886-1–27, 2023. (arXiv:2010.01072, DOI: 10.1016/j.aim.2023.108886)
M. Bischoff, S. Del Vecchio, L. Giorgetti. Compact hypergroups from discrete subfactors. J. Funct. Anal., 281:109004-1–78, 2021. (arXiv:2007.12384, DOI: 10.1016/j.jfa.2021.109004)
L. Giorgetti. Compact hypergroups from discrete subfactors. In Subfactors and Applications. Oberwolfach Rep., 16:3087–3092, 2019. (DOI: 10.4171/OWR/2019/49)
S. Del Vecchio, F. Fidaleo, L. Giorgetti, S. Rossi. Ergodic properties of the Anzai skew-product for the noncommutative torus. Ergodic Theory Dynam. Systems, 41:1064–1085, 2021. (arXiv:1910.11839, DOI: 10.1017/etds.2019.116)

Dissemination activities

Scientific seminars

05-08.07.2022 Matera: FAATNA22, Funct Analysis, Approx Theory and Num Analysis (invited talk)
03.03.2022 UQSL Seminar: University Quantum Symmetries Lectures (invited talk)
03.12.2021 Roma, Tor Vergata: OA Seminar PA description of conditional expectations (talk)
16-20.08.2021 Lancaster, UK: Workshop IWOTA 2021, Quantum groups and AQFT (invited talk)
05.05.2021 University of Nottingham, UK: Quantum Mathematics Seminar (invited talk)
09.04.2021 Ohio State, US: QSSS Quantum Symmetries Student Seminar (invited talk)
23.02.2021 UC Riverside, US: OA Seminar Compact hypergroups from discrete subfactors (talk)
21-28.01.2021 IPAM UCLA, US: Actions of Tensor Categories on C*-algebras (invited talk)
20.11.2020 Nashville, TN, US, Vanderbilt: Subfactor Seminar Distortion for multifactors (talk)
17-18.10.2020 University of Virginia, US: Workshop ECOAS 2020 (invited talk)
04-07.12.2019 Roma, Tor Vergata: Workshop Operator algebras in QFT & quantum probability (invited talk)
27.10-02.11.2019 Oberwolfach, MFO: Workshop 1944 Subfactors and applications (invited talk)
06-15.10.2019 Columbus, Ohio State, US: Compact hypergroups from discrete subfactors (talk)
13.09.2019 Nashville, TN, US, Vanderbilt: Subfactor Seminar Minimal index and dimension (talk)

Broader audience

05.12.2019 Roma, Tor Vergata: Meeting with the students MSCA day Tor Vergata (talk)

Google Sites

Report abuse