Related papers: Conformal Transformations as Observables
The conventional model of the gauge vector field is invariant under the local conformal symmetry only in the four-dimensional space ($4d$). Conformal generalization to an arbitrary dimension $d$ is impossible even for the free theory,…
New examples of N=2 supersymmetric conformal field theories are found as fixed points of SU(2) N=2 supersymmetric QCD. Relations among the scaling dimensions of their relevant chiral operators, global symmetries, and Higgs branches are…
Higher order conformal perturbation theory is studied for theories with and without boundaries. We identify systematically the universal quantities in the beta function equations, and we give explicit formulae for the universal coefficients…
Six-dimensional conformal field theories with $(2,0)$ supersymmetry are shown to possess a protected sector of operators and observables that are isomorphic to a two-dimensional chiral algebra. We argue that the chiral algebra associated to…
We review various aspects of two dimensional conformal field theories paying close attention to the algebraic structures that intervene. We provide a compact description regarding the appearance of a chiral algebra as the symmetry algebra…
We derive a bound on the conformal dimensions of the lightest few states in general unitary 2d conformal field theories with discrete spectra using modular invariance, including CFTs with chiral currents. We derive a bound on the conformal…
We develop the idea of an effective conformal theory describing the low-lying spectrum of the dilatation operator in a CFT. Such an effective theory is useful when the spectrum contains a hierarchy in the dimension of operators, and a small…
A modular invariant for a chiral conformal field theory is physical if there is a full conformal field theory with the given chiral halves realising the modular invariant. The easiest modular invariants are the charge conjugation and the…
This is the second of three papers on Conformal General Relativity (CGR). The conformal group is introduced here as the invariance group of the partial order of causal events in $n$D spacetime. Its general structure, discrete symmetries and…
Various definitions of chiral observables in a given Moebius covariant two-dimensional theory are shown to be equivalent. Their representation theory in the vacuum Hilbert space of the 2D theory is studied. It shares the general…
The modular commutator is a recently discovered multipartite entanglement measure that quantifies the chirality of the underlying many-body quantum state. In this Letter, we derive a universal expression for the modular commutator in…
This note supplements an earlier paper on conformal field theories. There it was shown how to construct tensor, spinor, and spinor-tensor primary fields in four dimensions from their counterparts in six dimensions, where conformal…
Some mathematical questions relating to Coset Conformal Field Theories (CFT) are considered in the framework of Algebraic Quantum Field Theory as developed previously by us. We consider the issue of fixed point resolution in the diagonal…
We argue that all consistent 4D quantum field theories obey a spacetime-averaged weak energy inequality $\langle T^{00} \rangle \ge -C/L^4$, where $L$ is the size of the smearing region, and $C$ is a positive constant that depends on the…
We investigate the gauge dynamics of nonsupersymmetric SU(N) gauge theories featuring the simultaneous presence of fermionic matter transforming according to two distinct representations of the underlying gauge group. We bound the regions…
Conformal transformations of the following kinds are compared: (1) conformal coordinate transformations, (2) conformal transformations of Lagrangian models for a D-dimensional geometry, given by a Riemannian manifold M with metric g of…
A new topological conformal field theory in four Euclidean dimensions is constructed from N=4 super Yang-Mills theory by twisting the whole of the conformal group with the whole of the R-symmetry group, resulting in a theory that is…
We construct novel conformal sigma models in three dimensions. Nonlinear sigma models in three dimensions are nonrenormalizable in perturbation theory. We use Wilsonian renormalization group equation method to find the fixed points.…
We present a general construction of all correlation functions of a two-dimensional rational conformal field theory, for an arbitrary number of bulk and boundary fields and arbitrary topologies. The correlators are expressed in terms of…
The main result of this paper is the construction of a conformally covariant operator in two dimensions acting on scalar fields and containing fourth order derivatives. In this way it is possible to derive a class of Lagrangians invariant…