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In this thesis we analyse three aspects of Conformal Field Theories (CFTs). First, we consider correlation functions of descendant states in two-dimensional CFTs. We discuss a recursive formula to calculate them and provide a computer…
All unitary Rational Conformal Field Theories (RCFT) are conjectured to be related to unitary coset Conformal Field Theories, i.e., gauged Wess-Zumino-Witten (WZW) models with compact gauge groups. In this paper we use subfactor theory and…
We consider Weyl's conformal gravity coupled to a complex matter field in Weyl geometry. It is shown that a Higgs potential naturally arises from a $\tilde R^2$ term in moving from the Jordan frame to the Einstein frame. A massless…
A gauge theory of gravity based on a nonlinear realization (NLR) of the local Conform-Affine (CA) group of symmetry transformations is presented. The coframe fields and gauge connections of the theory are obtained. The tetrads and Lorentz…
The Maxwell extension of the conformal algebra is presented. With the help of gauging the Maxwell-conformal group, a conformally invariant theory of gravity is constructed. In contrast to the conventional conformally invariant actions, our…
We develop a manifestly conformal approach to describe linearised (super)conformal higher-spin gauge theories in arbitrary conformally flat backgrounds in three and four spacetime dimensions. Closed-form expressions in terms of gauge…
This is the first of three papers on Conformal General Relativity (CGR), which differs from Einstein's General Relativity (GR) in that it requires action--integral invariance under local scale transformations in addition to general…
The conformal anomaly for 4D gravity-matter theories, which are non-minimally coupled with the dilaton, is systematically studied. Special care is taken for: rescaling of fields, treatment of total derivatives, hermiticity of the system…
In absence of matter Einstein gravity with a cosmological constant $\La$ can be formulated as a scale-free theory depending only on the dimensionless coupling constant G \Lambda where G is Newton constant. We derive the conformal field…
We discuss various aspects of anisotropic gravity in $(d+D)$-dimensional spacetime where $D$ dimensions are treated as extra dimensions. It is based on the foliation preserving diffeomorphism invariance and anisotropic conformal invariance.…
We review (non-supersymmetric) gauge theories of four-dimensional space-time symmetries and their quadratic action. The only true gauge theory of such a symmetry (with a physical gauge boson) that has an exact geometric interpretation,…
Weyl conformal geometry may play a role in early cosmology where effective theory at short distances becomes conformal. Weyl conformal geometry also has a built-in geometric Stueckelberg mechanism: it is broken spontaneously to Riemannian…
This is a shortened version of an invited talk at the XIII International Workshop "Lie Theory and its Applications in Physics", June 17-23, Varna, Bulgaria. A covariant canonical gauge theory of gravity free from torsion is studied. Using a…
We examine some Weyl invariant cosmological models in the framework of generalized dilaton gravity, in which the action is made of a set of $N$ conformally coupled scalar fields. It will be shown that when the FRW ansatz for the spacetime…
Conformal loop quantum gravity provides an approach to loop quantization through an underlying conformal structure i.e. conformally equivalent class of metrics. The property that general relativity itself has no conformal invariance is…
Conformal theories in a d dimensional spacetime may be expressed as manifestly conformal theories in a d+2 dimensional conformal space as first proposed by Dirac. The reduction to d dimensions goes via the d+1 dimensional hypercone in the…
Symmetric teleparallel gravity (STG) is a gravity theory which takes non-metricity tensor to describe gravity effects. In the STG framework, we study the conformal equivalent scalar-tensor theory of f(Q) model and calculate the cosmological…
We calculate the Weyl anomaly for conformal field theories that can be described via the adS/CFT correspondence. This entails regularizing the gravitational part of the corresponding supergravity action in a manner consistent with general…
A Lagrangian depending on geometric variables (metric, affine connection, gauge group generators) is given which maintains compatibility with General Relativity. It generates the dynamics for Electromagnetism and other Gauge Fields along…
In the framework of ordinary-derivative approach, conformal gravity in space-time of dimension six is studied. The field content, in addition to conformal graviton field, includes two auxiliary rank-2 symmetric tensor fields, two…