Related papers: How to understand the Structure of Beta Functions …
The aim of the current paper is to study the multiscalar-tensor theories of gravity without derivative couplings. We construct a few basic objects that are invariant under a Weyl rescaling of the metric and transform covariantly when the…
We introduce the beta function of a knot in euclidean three-space. This is a meromorphic function of a complex variable which we prove admits a Bernstein type functional equation. We determine the first residues.
We consider generalized diffeomorphisms on an extended mega-space associated to the U-duality group of gauged maximal supergravity in four dimensions, E_7. Through the bein for the extended metric we derive dynamical (field-dependent)…
One of the main advantages of super-renormalizable higher derivative quantum gravity models is the possibility to derive exact beta functions, by making perturbative one-loop calculations. We perform such a calculation for the Newton…
We propose a superspace formulation of N=(1,0) conformal supergravity in six dimensions. The corresponding superspace constraints are invariant under super-Weyl transformations generated by a real scalar parameter. The known variant Weyl…
We give a review of the one-loop divergences in higher derivative gravity theories. We first make the bilinear expansion in the quantum fluctuation on arbitrary backgrounds, introduce a higher-derivative gauge fixing and show that…
We discuss lowering the order of the two-dimensional scalar-tensor $R^2$ quantum gravity, by mapping the most general version of the model to a multi-dilaton gravity, which is essentially the sigma-model coupled with Jackiw-Teitelboim-like…
We study the Weyl vector fields which can play an important role in quantum gravity. The metric obtains its dynamical content after dynamical symmetry breaking in the phase of the effective Einstein gravity which is induced by quantum Weyl…
The main purpose of this work is to characterize derivations through functional equations. This work consists of five chapters. In the first one, we summarize the most important notions and results from the theory of functional equations.…
The on shell equivalence of first order and second order formalisms for the Einstein-Hilbert action does not hold for those actions quadratic in curvature. It would seem that by considering the connection and the metric as independent…
This paper aims to revisit the mathematical foundations of both General Relativity and Electromagnetism after one century, in the light of the formal theory of systems of partial differential equations and Lie pseudogroups (D.C. Spencer,…
We present the complete set of universal one-loop beta functions of cubic gravity in six dimensions. The system admits over 8000 distinct fixed points, of which more than 200 are real. Some of them might be relevant for the quantisation of…
By explicit solution of the one-loop finiteness conditions for all dimensionless coupling constants (i.~e., gauge coupling constant as well as Yukawa and quartic scalar-boson self-interaction coupling constants), two classes of grand…
We survay our recent results on fractional gravity theory. It is also provided the Main Theorem on encoding of geometric data (metrics and connections in gravity and geometric mechanics) into solitonic hierarchies. Our approach is based on…
The tensors which may be defined on the conformal manifold for six dimensional CFTs with exactly marginal operators are analysed by considering the response to a Weyl rescaling of the metric in the presence of local couplings. It is shown…
In this work we take into consideration a generalization of Gauge Theories based on the analysis of the structural characteristics of Maxwell theory, which can be considered as the prototype of such kind of theories (Maxwell-like). Such…
We address the construction of manifest U-duality invariant generalized diffeomorphisms. The closure of the algebra requires an extension of the tangent space to include a tensor hierarchy indicating the existence of an underlying unifying…
Recently, evidence was provided for the existence of an $a$-function for renormalisable quantum field theories in three dimensions. An explicit expression was given at lowest order for general theories involving scalars and fermions, and…
We discuss the long-distance physics of 2d adjoint QCD when it is viewed as an effective field theory, and determine the beta functions for its two classically-marginal four-fermi operators. These four-fermion terms preserve the invertible…
The renormalisation group equation for $N$-point correlation functions can be interpreted in a geometrical manner as an equation for Lie transport of amplitudes in the space of couplings. The vector field generating the diffeomorphism has…