Within the algebraic setting of quantum field theory, a condition is given which implies that the intersection of algebras generated by field operators localized in wedge--shaped regions of two--dimensional Minkowski space is non--trivial; in particular, there exist compactly localized operators in such theories which can be interpreted as local observables. The condition is based on spectral (nuclearity) properties of the modular operators affiliated with wedge algebras and the vacuum state and is of interest in the algebraic approach to the formfactor program, initiated by Schroer. It is illustrated here in a simple class of examples.
In the framework of Algebraic Quantum Field Theory, several operator algebraic notions of entanglement entropy can be associated to a couple of causally disjoint and distant spacetime regions $\mathcal{S}_A$ and $\mathcal{S}_B$. In this work, we show that the mutual information is finite in any local QFT verifying a modular $p$-nuclearity condition for some $0 < p <1$. A similar result is proved for another recently studied entanglement measure. Furthermore, if we assume conformal covariance then by comparison with other entanglement measures we can state that the mutual information satisfies …
Modular wedge localization, Majorana fields and the Tsirelson limit of the Bell-CHSH inequality
Universidade Federal Rural do Rio de Janeiro（里约热内卢联邦农村大学）；Universidade do Estado do Rio de Janeiro（里约热内卢州立大学）；Centro Brasileiro de Pesquisas Físicas（巴西物理研究中心）；ETH Zürich（苏黎世联邦理工学院）
We study the 2D vertex operator algebra (VOA) construction in 4D $\mathcal{N}=2$ superconformal field theories (SCFT) on $S^3 \times S^1$, focusing both on old puzzles as well as new observations. The VOA lives on a two-torus $\mathbb{T}^2\subset S^3\times S^1$, it is $\frac12\mathbb{Z}$-graded, and this torus is equipped with the natural choice of spin structure (1,0) for the $\mathbb{Z} +\frac12$-graded operators, corresponding to the NS sector vacuum character. By analyzing the possible refinements of the Schur index that preserve the VOA, we find that it admits discrete deformations, which…
Localization and the interface between quantum mechanics, quantum field theory and quantum gravity I (The two antagonistic localizations and their asymptotic compatibility)
