Related papers: Conformal Transformations as Observables
We study inclusions of local, chiral, conformal quantum theories C which are contained in an ambient theory B and commute with another given subtheory A. These subtheories C are called Coset models. Most of our results are…
Every locally normal representation of a local chiral conformal quantum theory is covariant with respect to global conformal transformations, if this theory is diffeomorphism covariant in its vacuum representation. The unitary, strongly…
Chiral orbifold models are defined as gauge field theories with a finite gauge group $\Gamma$. We start with a conformal current algebra A associated with a connected compact Lie group G and a negative definite integral invariant bilinear…
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…
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:…
Old folklore says that there is no non-trivial renormalization group fixed point with $U(1)$ gauge symmetry in four dimensions, but it can be circumvented by the existence of magnetic monopoles. We propose to construct (potentially…
Unitary conformal field theories (CFTs) are believed to have positive (non-negative) energy correlators. Energy correlators are universal observables in higher-dimensional CFTs built out of integrated Wightman functions of the stress-energy…
$Vect(N)$, the algebra of vector fields in $N$ dimensions, is studied. Some aspects of local differential geometry are formulated as $Vect(N)$ representation theory. There is a new class of modules, {\it conformal fields}, whose…
It has long been clear that the conformal bootstrap is associated with a rich geometry. In this paper we undertake a systematic exploration of this geometric structure as an object of study in its own right. We study conformal blocks for…
We study 2+1 dimensional conformal field theories (CFTs) with a globally conserved U(1) charge, placed in a chemical potential which is periodically modulated along the spatial direction $x$ with zero average: $\mu(x) = V \cos(kx)$. The…
We show that any positive energy projective unitary representation of Diff(S^1) extends to a strongly continuous projective unitary representation of the fractional Sobolev diffeomorphisms D^s(S^1) for any real s>3, and in particular to…
We study the general form of M"obius covariant local commutation relations in conformal chiral quantum field theories and show that they are intrinsically determined up to structure constants, which are subject to an infinite system of…
We introduce a new class of two dimensional conformal field theories by extending Wess-Zumino-Witten (WZW) models to chiral algebras with matrix-valued levels. The new CFTs are based on holomorphic currents with an operator product…
The superselection sectors of two classes of scalar bilocal quantum fields in D>=4 dimensions are explicitly determined by working out the constraints imposed by unitarity. The resulting classification in terms of the dual of the respective…
Conformal defects describe the universal behaviors of a conformal field theory (CFT) in the presence of a boundary or more general impurities. The coupled critical system is characterized by new conformal anomalies which are analogous to,…
We study general perturbations of two-dimensional conformal field theories by holomorphic fields. It is shown that the genus one partition function is controlled by a contact term (pre-Lie) algebra given in terms of the operator product…
Majorana's arbitrary spin theory is considered in a hyperbolic complex representation. The underlying differential equation is embedded into the gauge field theories of Sachs and Carmeli. In particular, the approach of Sachs can serve as a…
Given a local quantum field theory net A on the de Sitter spacetime dS^d, where geodesic observers are thermalized at Gibbons-Hawking temperature, we look for observers that feel to be in a ground state, i.e. particle evolutions with…
We study conformal field theories (CFTs) on curved spaces including both orientable and unorientable manifolds possibly with boundaries. We first review conformal transformations on curved manifolds. We then compute the identity components…
This is an invited contribution to the 2nd edition of the Encyclopedia of Mathematical Physics. We review the following algebraic structures which appear in two-dimensional conformal field theory (CFT): The symmetries of two-dimensional…