Related papers: Explicit Examples on Conformal Invariance
By twisting the commutation relations between creation and annihilation operators, we show that quantum conformal invariance can be implemented in the 2-d Moyal plane. This is an explicit realization of an infinite dimensional symmetry as a…
Several aspects of fusion rings and fusion rule algebras, and of their manifestations in twodimensional (conformal) field theory, are described: diagonalization and the connection with modular invariance; the presentation in terms of…
Conformal symmetry always played an important role in field theory (both quantum and classical) and in gravity. We present construction of quantum conformal gravity and discuss its features regarding scattering amplitudes and quantum…
It is generally taken for granted that two-dimensional critical phenomena can be fully classified by the well known two-dimensional (rational) conformal quantum field theories (CQFTs). In particular it is believed that in models with a…
It is found that the induced gravity with conformal couplings requires the conformal invariance in both classical and quantum levels for consistency. This is also true for the induced gravity with an extended conformal coupling interacting…
We give new solutions of the quantum conformal deformations of the full Maxwell equations in terms of deformations of the plane wave. We study the compatibility of these solutions with the conservation of the current. We also start the…
Logarithmic conformal field theories have a vast range of applications, from critical percolation to systems with quenched disorder. In this paper we thoroughly examine the structure of these theories based on their symmetry properties. Our…
We will report some results concerning the Yamabe problem and the Nirenberg problem. Related topics will also be discussed. Such studies have led to new results on some conformally invariant fully nonlinear equations arising from geometry.…
Without a complete theory of quantum gravity, the question of how quantum fields and quantum particles behave in a superposition of spacetimes seems beyond the reach of theoretical and experimental investigations. Here we use an extension…
By adapting previously known arguments concerning Ricci flow and the c-theorem, we give a direct proof that in a two-dimensional sigma-model with compact target space, scale invariance implies conformal invariance in perturbation theory.…
We discuss a novel form of the variational approach in Quantum Field Theory in which the trial quantum configuration is represented directly in terms of relevant expectation values rather than, e.g., increasingly complicated structure from…
We present a new framework for a Lagrangian description of conformal field theories in various dimensions based on a local version of d+2-dimensional conformal space. The results include a true gauge theory of conformal gravity in d=(1,3)…
We analyze conformal gravity in translationally invariant approximation, where the metric is taken to depend on time but not on spatial coordinates. We find that the field mode which in perturbation theory has a ghostlike kinetic term,…
In the large N limit, conditions for the conformal invariance of the generalized Thirring model are derived, using two different approaches: the background field method and the Hamiltonian method based on an operator algebra, and 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,…
The immediate purpose of the paper was neither to review the basic definitions of percolation theory nor to rehearse the general physical notions of universality and renormalization (an important technique to be described in Part Two). It…
In this outline of a program, based on rigorous renormalization group theory, we introduce new definitions which allow one to formulate precise mathematical conjectures related to conformal invariance as studied by physicists in the area…
In a first part, we generalize a theorem for an holomorphic $\times $ anti-holomorphic integrand, in the case of 2 dimensional Fourier transform. In the second part, we derive p-uple conformal integrals the integrand of which are linear…
A class of parametric functions formed by alternating compositions of multivariate polynomials and rectification style monomial maps is studied (the layer-wise exponents are treated as fixed hyperparameters and are not optimized). For this…
We propose fundamental scale invariance as a new theoretical principle beyond renormalizability. Quantum field theories with fundamental scale invariance admit a scale-free formulation of the functional integral and effective action in…