相关论文: Conformal Nets, Maximal Temperature and Models fro…

We analyze the set of locally normal KMS states w.r.t. the translation group for a local conformal net A of von Neumann algebras on R. In this first part, we focus on completely rational net A. Our main result here states that, if A is…

We describe the role conformal nets, a mathematical model for conformal field theory, could play in a geometric definition of the generalized cohomology theory TMF of topological modular forms. Inspired by work of Segal and Stolz-Teichner,…

We describe a coordinate-free perspective on conformal nets, as functors from intervals to von Neumann algebras. We discuss an operation of fusion of intervals and observe that a conformal net takes a fused interval to the fiber product of…

We describe a coordinate-free notion of conformal nets as a mathematical model of conformal field theory. We define defects between conformal nets and introduce composition of defects, thereby providing a notion of morphism between…

Conformal nets provide a mathematical formalism for conformal field theory. Associated to a conformal net with finite index, we give a construction of the `bundle of conformal blocks', a representation of the mapping class groupoid of…

We analyze the finite temperature behaviour of massless conformally coupled scalar fields in homogeneous lens spaces $S^3/{\mathbb Z}_p$. High and low temperature expansions are explicitly computed and the behavior of thermodynamic…

We explore new connections between the fields and local observables in two dimensional chiral conformal field theory. We show that in a broad class of examples, the von Neumann algebras of local observables (a conformal net) can be obtained…

We study the $t$-deformation of gaussian von Neumann algebras. They appear as example in the theories of Interacting Fock spaces and conditionally free products. When the number of generators is fixed, it is proved that if $t$ sufficiently…

We apply an idea of framed vertex operator algebras to a construction of local conformal nets of (injective type III_1) factors on the circle corresponding to various lattice vertex operator algebras and their twisted orbifolds. In…

We derive new closed form expressions for the partition functions of free conformally-coupled scalars on $S^{2D-1}\times S^1$ which resum the exact high-temperature expansion. The derivation relies on an identification of the partition…

Starting with a conformal Quantum Field Theory on the real line, we show that the dual net is still conformal with respect to a new representation of the Moebius group. We infer from this that every conformal net is normal and conormal,…

We have shown that a particular class of non-local free field theory has conformal symmetry in arbitrary dimensions. Using the local field theory counterpart of this class, we have found the Noether currents and Ward identities of the…

Let $R$ be a finitely generated positively graded algebra over a Noetherian local ring $B$, and $\mathfrak{m} = [R]_+$ be the graded irrelevant ideal of $R$. We provide a local criterion characterizing the $B$-freeness of all the local…

In this article we give new examples of models in boundary quantum field theory, i.e. local time-translation covariant nets of von Neumann algebras, using a recent construction of Longo and Witten, which uses a local conformal net A on the…

Let $\mathcal{R}$ be a free Lie conformal algebra of rank $2$ with $\mathbb{C}[\partial]$-basis $\{L,I\}$ and relations \begin{eqnarray*} \left[L_{\lambda} L\right]=(\partial+2 \lambda) (L+I),\ \left[L_{\lambda} I\right]=(\partial+\lambda)…

The tight binding model is a minimalistic electronic structure model for predicting properties of materials and molecules. For insulators at zero Fermi-temperature we show that the potential energy surface of this model can be decomposed…

We study conformal field theories at finite temperature in the presence of a temporal conformal line defect, wrapping the thermal circle, akin to a Polyakov loop in gauge theories. Although several symmetries of the conformal group are…

We show that a class of $L$-loop conformal ladder graphs correspond to twisted partition functions of free massive complex scalars in $d=2L+1$ dimensions. The graphs arise as four-point functions in certain two- and four-dimensional…

We adapt the bialgebra and Hopf relations to expose internal structure in the ground state of a Hamiltonian with $Z_2$ topological order. Its tensor network description allows for exact contraction through simple diagrammatic rewrite rules.…

We consider unitary simple vertex operator algebras whose vertex operators satisfy certain energy bounds and a strong form of locality and call them strongly local. We present a general procedure which associates to every strongly local…