Detlev Buchholz (slides)
Arrow of time and quantum physics
In the framework of local quantum physics, the hypothesis is discussed that the (non-reversible) arrow of time is intrinsic to all systems, no matter how small they are. It is shown how such a semigroup action of time can be extended consistently to that of the group of spacetime translations in Minkowski space. In the presence of massless excitations, however, ambiguities arise in the theoretical extension of the time translations to the past. The corresponding loss of quantum information about states over time is determined. Finally, it is explained how the description of local operations in classical terms combined with causal constraints by the arrow of time leads to a quantum theoretical framework. These results suggest that the arrow of time is fundamental in nature and not merely a consequence of statistical effects on which the Second Law is based. [Joint work with Klaus Fredenhagen.]
Bin Gui (slides)
Strong locality and equivalence of representation categories for VOA extensions
A systematic study of the relationship between unitary VOAs and conformal nets was initiated by Carpi-Kawahigashi-Longo-Weiner. A central condition in their approach is strong locality, which says roughly that the smeared vertex operators localized on disjoint intervals of the unit circle commuted strongly in the sense that the vN algebras generated by them commute. Many useful criteria on strong locality have been established in that work and in subsequent work, but most of them are not applicable to extensions of VOA. In this talk, I will explain how to prove strong locality for (conformal) extensions of many strongly rational unitary VOAs.
Stefan Hollands
Anyonic Chains and von Neumann Algebras
Anyonic spin chains have been introduced in theoretical physics as models for topological quantum computation. There is evidence that their scaling limits can give -- among other things -- rational CFTs in 1+1 dimensions, including conjecturally novel classes of CFTs inaccessible by traditional methods. I this talk I show that anyonic spin chain models have a very large mathematical overlap with subfactor theory of von Neumann algebras. This leads in turn to the construction of novel symmetry and defect operators in the model. It is surprising that the mathematical structure describing the latter turns out to be isomorphic to the structures unveiled by Bischoff, Kawahigashi, Longo, Rehren in rational 1+1 CFTs -- even more so since anyonic chains are fundamentally discrete and not necessarily tied to conformal symmetry.
Masaki Izumi
Several infinite families of potential modular data
Every modular tensor category gives rise to a representation of the modular group as an invariant, called modular data. Based on our computation of modular data of Drinfeld centers for quadratic categories, we discovered several infinite families of new potential modular data generalizing Evans-Gannon's family. Some of them suggest the existence of a new class of quadratic categories, and we report on our recent attempt to realize them. This is joint work with Pinhas Grossman.
Arthur M. Jaffe
A Quantum Central Limit Theorem
A new convolution for discrete-variable quantum systems leads to a quantum central limit theorem. Stabilizer states play the role of classical Gaussians. This gives a mathematical framework for property testing. I describe recent joint work with Kaifeng Bu and Weichen Gu.
Victor Kac
Unitary representations of minimal W-algebras.
To each non-zero nilpotent orbit of a simple finite-dimensional Lie superalgebra g with a non-degenerate even invariant bilinear form one associates a simple vertex algebra,called a W-algebra. In the simplest case g=sl(2) one gets the Virasoro vertex algebra. For the smallest simple Lie superalgebras one gets all N=1,2,3,4, and big N=4 superconformal algebras. I will explain classification of unitary representations of W-algebras, associated to minimal nilpotent orbits of basic simple Lie superalgebras,which cover all the above examples. This is a joint work with P. Moseneder Frajria and P. Papi.
Yasuyuki Kawahigashi
Alpha-induction for bi-unitary connections
Alpha-induction is a tensor functor associated with a Q-system (Frobenius algebra) in a modular tensor category. This has been studied in the contexts of chiral conformal field theory and abstract braided fusion categories. From an operator algebraic viewpoint, this gives an induction procedure for bimodules and endomorphisms. We now give a new formulation based on bi-unitary connections in subfactor theory. Bi-unitary connections are certain 4-tensors and their relations to 2-dimensional topological order have been recently studied.
Gandalf Lechner (slides)
Standard subspaces and twisted Araki-Woods factors
Guided by the main principles of quantum field theory; locality, covariance, and interaction, in this talk I will discuss twisted Araki-Woods factors which are built on the basis of a standard subspace (encodes a localization region) and a twist (encodes a two-particle interaction) in a functorial manner. As appropriate for the occasion, this talk will on the one hand include various links to the work of Roberto Longo and on the other hand connect to both mathematical physics (quantum field theory) and von Neumann algebras (subfactors). In particular, it will be explained how twists with a cyclic and separating vacuum vector can be characterized, and which properties of twists and standard subspaces imply large relative commutants of subfactors built from inclusions of standard subspaces. Joint work with Ricardo Correa da Silva.
Yoshiko Ogata
Operator algebraic approach to topological phases
Recently, topological orders in quantum many-body systems have attracted a lot of attention. In this talk, I would like to explain our operator algebraic approach to this problem. The operator algebraic approach allows us to think of the problem in the general setting of gapped ground state phases, in a mathematically rigorous manner.
Hirosi Ooguri (slides)
Symmetry Resolution at High Energy
The density of states of a unitary conformal field theory is known to have a universal behavior at high energy. In two dimensions, this behavior is described by the Cardy formula. When the theory has symmetry, the Hilbert space can be decomposed into irreducible representation of the symmetry. In this talk, I will derive universal formulas for the decomposition of states at high energy with respect to both internal global symmetry and spacetime symmetry. The generalized Noether theorem proven by Professor Longo and his collaborators plays an important role in the decomposition. The formulae are applicable to any unitary conformal field theory in any spacetime dimensions. As a byproduct, we resolve one of the outstanding questions on the stability of non-abelian black holes. We will also derive the high energy asymptotic behavior of correlation functions. (Based on work with Nathan Benjamin, Daniel Harlow, Monica Kang, Jaeha Lee, Sridip Pal, David Simmons-Duffin, Zhengdi Sun, and Zipei Zhang.)
Sorin Popa
Non-isomorphism of A*n, 2 ≤ n ≤ ∞, for a non-separable Abelian von Neumann algebra A
I will present some recent joint work with Remi Boutonnet, Daniel Drimbe and Adrian Ioana, in which we prove that if A is a non-separable Abelian von Neumann algebra then its free powers A*n, 2 ≤ n ̸= ∞, are non-isomorphic, with trivial fundamental group, F(A*n)=1, whenever n< ∞.
Kasia Rejzner (slides)
Nets of local algebras for interacting QFT: from perturbative to non-perturbative
In this talk I will give a status report on the progress in studying interacting QFTs using the construction proposed by Buchholz and Fredenhagen in 2019. The idea is to define local algebras as C*-algebras generated by unitaries with the interpretation of local S-matrices. In the course of a joint project with Brunetti, Duetsch and Fredenhagen, we have seen how to implement dynamics, the time-slice axiom and symmetries (in the form of the anomalous Noether theorem).
Jean-Luc Sauvageot (slides)
A noncommutative Sierpinski Gasket
A quantized version of the Sierpinski gasket is proposed, on purely topological grounds, as a C∗-algebra A∞ with a suitable form of self-similarity. Several properties of A∞ are studied, in particular its nuclearity, the structure of ideals as well as the description of irreducible representations and extremal traces. A harmonic structure is introduced, giving rise to a self-similar Dirichlet form Ɛ. A spectral triple is also constructed, extending the one already known for the classical gasket, from which Ɛ can be reconstructed. Moreover we show that A∞ is a compact quantum metric space. This is joint work with Fabio Cipriani, Daniele Guido and Tommaso Isola.
Mihály Weiner (slides)
Orthogonal systems of Abelian subalgebras and finite geometry
In many quantum information theoretical protocols one needs a collection of physical quantities satisfying the following condition: if the state is such that one of these quantities has a certain value, then all other quantities are maximally uncertain. This led to the concept and study of "mutually unbiased bases"; collections of pairwise orthogonal maximal abelian *-subalgebras of a finite dimensional matrix algebra (although they have been considered in the type II_1 setting, too). While studying actual examples, many curious similarities have been noted between mutually unbiased bases and some classical finite geometrical objects. Recently, in a joint work with Szilágyi and Nietert we observed that with the right generalization and setting, those classical structures become the commutative versions of mutually unbiased bases. We then used this common (C*-algebra) setting to prove a certain rigidity property, which - due to the common framework - automatically applies to both structures.
Feng Xu (slides)
Rigorous results about entropies in QFT
I will discuss some recent results about relative entropies in QFT, with particular emphasis on the singular limits of such entropies.