Related papers: Coends in conformal field theory
Linking systems were introduced to provide algebraic models for $p$-completed classifying spaces of fusion systems. Every linking system over a saturated fusion system $\mathcal{F}$ corresponds to a group-like structure called a locality.…
The notion of a categorical quotient can be generalized since its standard categorical concept does not recover the expected quotients in certain categories. We present a more general formulation in the form of $\mathcal{F}$-quotients in a…
The quantization of vector bundles is defined. Examples are constructed for the well controlled case of equivariant vector bundles over compact coadjoint orbits. (Coadjoint orbits are symplectic spaces with a transitive, semisimple symmetry…
Functor coalgebras capture a wide range of transition systems that must however evolve in discrete steps. We introduce graded coalgebras of graded monads and propose them to model continuous-time transition systems. We develop the theory of…
Recently, quantum entanglement has been presented as a cohomological obstruction to reconstructing a global quantum state from locally compatible information, where sheafification provides a functor that is forgetful with regards to…
This is a brief summary of our studies of quantum field theories in a special limit in which the instantons are present, the anti-instantons are absent, and the perturbative corrections are reduced to one-loop. We analyze the corresponding…
We discuss conformal field theories (CFTs) in rectangular geometries, and develop a formalism that involves a conformal boundary state for the 1+1d open system. We focus on the case of homogeneous boundary conditions (no insertion of a…
We present recent progress in theory of local conformal nets which is an operator algebraic approach to study chiral conformal field theory. We emphasize representation theoretic aspects and relations to theory of vertex operator algebras…
I review three different problems occuring in two dimensional field theory: 1) classification of conformal field theories; 2) construction of lattice integrable realizations of the latter; 3) solutions to the WDVV equations of topological…
In the framework of locally covariant quantum field theory, a theory is described as a functor from a category of spacetimes to a category of *-algebras. It is proposed that the global gauge group of such a theory can be identified as the…
The concept of conformal field theory provides a general classification of statistical systems on two-dimensional geometries at the point of a continuous phase transition. Considering the finite-size scaling of certain special observables,…
Vertex algebras formalize the subalgebra of holomorphic fields of a conformal field theory. OPE-algebras were proposed as a generalization of vertex algebras that formalizes the algebra of all fields of a conformal field theory. We prove…
Groundstates of 1+1d conformal field theories (CFTs) satisfy a local entropic condition called the vector fixed point equation. This condition is surprisingly well satisfied by groundstates of quantum critical lattice models even at small…
The principle of local covariance which was recently introduced admits a generally covariant formulation of quantum field theory. It allows a discussion of structural properties of quantum field theory as well as the perturbative…
Entropies associated with spatial subsystems in conventional local quantum field theories are typically divergent when the spatial regions have boundaries. However, in certain linear combinations of the entropies for various subsystems,…
Quantum contextuality, a fundamental feature distinguishing quantum theory from classical models, is investigated via algebraic and topological structures inherent in modular tensor categories. This work rigorously demonstrates that braid…
In [Can et al. 2016], quantum Hall states on singular surfaces were shown to possess an emergent conformal symmetry. In this paper, we develop this idea further and flesh out details on the emergent conformal symmetry in holomorphic…
We construct a generalized class of quantum gravity condensate states, that allows the description of continuum homogeneous quantum geometries within the full theory. They are based on similar ideas already applied to extract effective…
A conformal field theory (CFT) is a quantum field theory which is invariant under conformal transformations; a group action that preserve angles but not necessarily lengths. There are two traditional approaches to the construction of CFTs:…
The orbifold construction via topological defects in quantum field theory can either be understood as a state sum construction internal to a given ambient theory, or as the procedure of (identifying and) gauging ordinary and…