Bohrification of operator algebras and quantum logic by Landsman, C, Spitters, B

ON FACTORIAL STATES OF OPERATOR-ALGEBRAS .3. by Archbold, R, Batty, C

ON FACTORIAL STATES OF OPERATOR-ALGEBRAS .2. by Batty, C, Archbold, R

OPERATOR ALGEBRA FOR STOCHASTIC DYNAMICS AND THE HEISENBERG CHAIN by Stinchcombe, R, Schutz, G

Deformation quantizations from vertex operator algebras by Pan, Y, Peelaers, W

“…In this note we address the question whether one can recover from the vertex operator algebra associated with a four-dimensional N = 2 superconformal field theory the deformation quantization of the Higgs branch of vacua that appears as a protected subsector in the three-dimensional circle-reduced theory. …”

Application of operator algebras to stochastic dynamics and the Heisenberg chain. by Stinchcombe, R, Schütz, G

Vertex operator algebras, Higgs branches, and modular differential equations by Beem, C, Rastelli, L

“…In this work, we aim to characterize the connection between the Higgs branch of the moduli space of vacua (as an algebraic geometric entity) and the associated vertex operator algebra. Ultimately our proposal is simple, but its correctness requires the existence of a number of nontrivial null vectors in the vacuum Verma module of the vertex operator algebra. …”

Bernoulli, Euler, permutations and quantum algebras by Hodges, A, Sukumar, C

“…The classification is naturally described by an operator algebra of a type familiar from quantum theory. …”

Flavor symmetries and unitarity bounds in N = 2 superconformal field theories by Beem, C

“…I derive several general and far-reaching consequences of unitarity by computing the norms of flavor singlet Higgs branch operators appearing in the squares of “moment map” operators via the associated vertex operator algebra, and imposing the requirement that they be non-negative.…”

A domain wall in twisted M-theory by Oh, J, Zhou, Y

“…We identify the classical algebra of operators on the domain wall in terms of a higher vertex operator algebra, which describes the holomorphic subsector of a 4d $\mathcal{N}$ = 1 supersymmetric field theory, and compute the associated mode algebra. …”

VOAs and rank-two instanton SCFTs by Beem, C, Meneghelli, C, Peelaers, W, Rastelli, L

“…We analyze the N=2 superconformal field theories that arise when a pair of D3-branes probe an F-theory singularity from the perspective of the associated vertex operator algebra. We identify these vertex operator algebras for all cases; we find that they have a completely uniform description, parameterized by the dual Coxeter number of the corresponding global symmetry group. …”

A geometric free field realisation for the genus-two class S theory of type a1 by Beem, C, Meneghelli, C

“…We present a free field realisation for the vertex operator algebra associated to the genus-two, class $\mathcal{S}$ superconformal field theory of type $\mathfrak{a}_1$. …”

Feynman diagrams and Ω-deformed M-theory by Oh, J, Zhou, Y

“…We derive the simplest commutation relations of operator algebras associated to M2 branes and an M5 brane in the Ω -deformed M-theory, which is a natural set-up for Twisted holography. …”

Twisted chiral algebras of class S and mixed Feigin-Frenkel gluing by Beem, C, Nair, S

“…The correspondence between four-dimensional N=2 superconformal field theories and vertex operator algebras, when applied to theories of class S, leads to a rich family of VOAs that have been given the monicker chiral algebras of class S. …”

Boundary conformal fields and Tomita--Takesaki theory by Hannabuss, K, Semplice, M

“…Motivated by formal similarities between the continuum limit of the Ising model and the Unruh effect, this paper connects the notion of an Ishibashi state in boundary conformal field theory with the Tomita--Takesaki theory for operator algebras. A geometrical approach to the definition of Ishibashi states is presented, and it is shownthat, when normalisable the Ishibashi states are cyclic separating states, justifying the operator state correspondence. …”

Free field realizations from the Higgs branch by Beem, C, Meneghelli, C, Rastelli, L

“…We present free field realizations for the associated vertex operator algebras of a number of four-dimensional N = 2 superconformal field theories. …”

Deformation Quantization and Superconformal Symmetry in Three Dimensions by Beem, C, Peelaers, W, Rastelli, L

“…We investigate the structure of certain protected operator algebras that arise in threedimensional N = 4 superconformal field theories. …”

Unified theory of local quantum many-body dynamics: eigenoperator thermalization theorems by Buča, B

“…Explaining quantum many-body dynamics is a long-held goal of physics. A rigorous operator algebraic theory of dynamics in locally interacting systems in any dimension is provided here in terms of time-dependent equilibrium (Gibbs) ensembles. …”

Contextuality and noncommutative geometry in quantum mechanics by De Silva, N, Barbosa, RS

“…Here, we consider the geometrically dual objects of noncommutative operator algebras of observables as being generalisations of classical (deterministic) state spaces to the quantum setting and argue that these generalised state spaces represent the objects of study of noncommutative operator geometry. …”