Calendar
- 09June 9, 2023
CMSA Quantum Matter in Mathematics and Physics: Classification of Self-Dual Vertex Operator Superalgebras of Central Charge at Most 24
We discuss the classification of self-dual vertex operator superalgebras (SVOAs) of central charge 24, or in physics parlance the purely chiral 2-dimensional fermionic conformal field theories with just one primary field.
There are exactly 969 such SVOAs under suitable regularity assumptions and the assumption that the shorter moonshine module VB^# is the unique self-dual SVOA of central charge 23.5 whose weight-1/2 and weight-1 spaces vanish.
We construct and classify the self-dual SVOAs by determining the 2-neighbourhood graph of the self-dual (purely bosonic) VOAs of central charge 24 and also by realising them as simple-current extensions of a dual pair containing a certain maximal lattice VOA. We show that all SVOAs besides VB^# x F and potential fake copies thereof stem from
elements of the Conway group Co_0, the automorphism group of the Leech lattice.By splitting off free fermions F, if possible, we obtain the classification for all central charges less than or equal to 24.
Reference: G. Höhn, S. Möller, arXiv:2303.17190.
For more information, please see:Quantum Matter in Mathematics and Physics (QMMP) 2023:
https://cmsa.fas.harvard.edu/event_category/quantum-matter- seminar/ ——–
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https://forms.gle/1ewa7KeP6BxBuBeRA - 13June 13, 2023
CMSA Quantum Matter in Mathematics and Physics Seminar: Small Bosonic CFTs, Chiral Fermionization, and Symmetry/Subalgebra Duality
Conformal field theories in (1+1)D are key actors in many dramas of physics and mathematics. Their classification has therefore been an important and long-standing problem. In this talk, I will explain the main ideas behind the classification of (most) “small” bosonic CFTs. Here, I use the adjective “small” informally to refer to theories with low central charge (less than 24) and few primary operators (less than 5). Time and attention permitting, I will highlight two applications of this result. First, I will describe how it can be used in tandem with bosonization and fermionization techniques to establish the classification of chiral fermionic CFTs with central charge less than 23. Second, I will showcase how it can be used to bootstrap generalized global symmetries using the concept of “symmetry/subalgebra duality.”Talk based on arXiv:2208.05486 [hep-th] (joint work with Sunil Mukhi) and arXiv:2303.16921 [hep-th].For more information, please see:Quantum Matter in Mathematics and Physics (QMMP) 2023:
https://cmsa.fas.harvard.edu/event_category/quantum-matter- seminar/ ——–
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https://forms.gle/1ewa7KeP6BxBuBeRA - 26June 26, 2023
CMSA Quantum Matter in Mathematics and Physics Seminar: Chiral fermionic CFTs of central charge ≤ 16
We classified all chiral fermionic CFTs of central charge ≤ 16 using Kac’s theorem and bosonization/fermionization. This talk will discuss the derivation of this result, its application to the classification of non-supersymmetric heterotic string theories, and along the way we’ll address some oft-overlooked subtleties of bosonization from the point of view of anomalies and topological phases.For more information, please see:Quantum Matter in Mathematics and Physics (QMMP) 2023:
https://cmsa.fas.harvard.edu/event_category/quantum-matter- seminar/ ——–
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https://forms.gle/1ewa7KeP6BxBuBeRA - 30June 30, 2023
CMSA Quantum Matter in Mathematics and Physics Seminar: Monopoles, Scattering, and Generalized Symmetries
In this talk, we will discuss the problem of electrically charged, massless fermions scattering off magnetic monopoles. The interpretation of the outgoing states has long been a puzzle, as they can carry fractional quantum numbers. We argue that such outgoing particles live in the twisted sector of a topological co-dimension 1 surface, which ends topologically on the monopole. This symmetry defect is often non-invertible, and as such the outgoing radiation not only carries unconventional flavor quantum numbers, but is often trailed by a topological field theory, which is a new prediction.For more information, please see:Quantum Matter in Mathematics and Physics (QMMP) 2023:
https://cmsa.fas.harvard.edu/event_category/quantum-matter- seminar/ ——–
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