Related papers: Vertex Operators in 4D Quantum Gravity Formulated …
In quantum gravity, physically meaningful operator is required to be invariant under the diffeomorphisms. Such gauge invariant operator is typically given by the relational observable, the operator localized in relation to some background…
Warped convolutions of operators were recently introduced in the algebraic framework of quantum physics as a new constructive tool. It is shown here that these convolutions provide isometric representations of Rieffel's strict deformations…
In this paper, we analyze the constraints imposed by unitarity and crossing symmetry on conformal theories in large dimensions. In particular, we show that in a unitary conformal theory in large dimension $D$, the four-point function of…
We present in the article the formulation of a version of Lorentz covariant quantum mechanics based on a group theoretical construction from a Heisenberg-Weyl symmetry with position and momentum operators transforming as Minkowski…
An anomaly-free operator corresponding to the Wheeler-DeWitt constraint of Lorentzian, four-dimensional, canonical, non-perturbative vacuum gravity is constructed in the continuum. This operator is entirely free of factor ordering…
We compute in closed analytical form the minimal set of "seed" conformal blocks associated to the exchange of generic mixed symmetry spinor/tensor operators in an arbitrary representation (l,\bar l) of the Lorentz group in four dimensional…
Conformal Quantum Field Theories (CFT) in 1 or 1+1 spacetime dimensions (respectively called chiral and full CFTs) admit several "axiomatic" (mathematically rigorous and model-independent) formulations. In this note, we deal with the von…
The three-point functions for minimal models coupled to gravity are derived in the operator approach to Liouville theory which is based on its $U_q(sl(2))$ quantum group structure. The result is shown to agree with matrix-model calculations…
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…
$T\bar{T}$-deformed CFTs are known to possess nonlocal conformal symmetries that do not act tractably on the undeformed local operators. In this paper, we explicitly construct two distinct classes of operators: (i) dressed operators, which…
In physics, it is believed that the consistency of two dimensional conformal field theory follows from the bootstrap equation. In this paper, we introduce the notion of a full vertex algebra by analyzing the bootstrap equation, which is a…
Conformal Gravity (CG) is a Weyl--invariant metric theory whose action is free from divergences for generic asymptotically anti-de Sitter spaces. For Neumann boundary conditions, it reduces to renormalized Einstein--AdS gravity at tree…
We study chiral vertex operators in the sine-Gordon [SG] theory, viewed as an off-conformal system. We find that these operators, which would have been primary fields in the conformal limit, have interesting and, in some ways, unexpected…
We study the map between two descriptions of the $T\bar{T}$ deformation of conformal field theory (CFT): One is the defining description as a deformation of CFT by the $T\bar{T}$-operator. The other is an alternative description as the…
We construct two-dimensional conformal field theories with a Z_N symmetry, based on the second solution of Fateev-Zamolodchikov for the parafermionic chiral algebra. Primary operators are classified according to their transformation…
We present a systematic exploration of conformal field theories (CFTs) constrained by duality-inspired fusion rules using the conformal bootstrap. We classify the operator spectrum into three sectors: $[\sigma]$, $[\epsilon]$, and $[1]$.…
We explore the constraining power of OPE associativity in 4D Conformal Field Theory with a continuous global symmetry group. We give a general analysis of crossing symmetry constraints in the 4-point function <Phi Phi Phi* Phi*>, where Phi…
An affine vertex operator construction at arbitrary level is presented which is based on a completely compactified chiral bosonic string whose momentum lattice is taken to be the (Minkowskian) affine weight lattice. This construction is…
We associate vertex operators to space-time diffeomorphisms in flat space string theory, and compute their algebra, which is a diffeomorphism algebra with higher derivative corrections. As an application, we realize the asymptotic symmetry…
The matrix normed structure of the unitization of a (non-selfadjoint) operator algebra is determined by that of the original operator algebra. This yields a classification up to completely isometric isomorphism of two-dimensional unital…