Related papers: A Conformal Fixed-Point Equation for the Effective…
Starting from a modified version of Polchinski's equation, Morris' fixed-point equation for the effective average action is derived. Since an expression for the line of equivalent fixed-points associated with every critical fixed-point is…
The class of effective actions exactly reproducing the conformal anomaly in 4D is considered. It is demonstrated that the freedom within this class can be fixed by the choice of the conformal gauge. The conformal invariant part of the…
The standard flow equation for the effective average action can be derived from a Legendre transform of Polchinski's exact renormalization group equation. However, the latter is not well adapted for finding fixed-points with non-zero…
We discuss the effective potential of the conformal factor in the effective average action approach to Quantum Einstein Gravity. Without invoking any truncation or other approximations we show that if the theory has has a non-Gaussian…
A new realization of the conformal algebra is studied which mimics the behaviour of a statistical system on a discrete albeit infinite lattice. The two-point function is found from the requirement that it transforms covariantly under this…
We summarize recent progress in the understanding of fixed point resolution for conformal field theories. Fixed points in both coset conformal field theories and non-diagonal modular invariants which describe simple current extensions of…
The term integrable asymptotically conformal at a point for a quasiconformal map defined on a domain is defined. Furthermore, we prove that there is a normal form for this kind attracting or repelling or super-attracting fixed point with…
Starting with conformally covariant correlation functions, a sequence of functional representations of the conformal algebra is constructed. A key step is the introduction of representations which involve an auxiliary functional. It is…
We present a truncation scheme of the effective average action approach of the nonperturbative renormalization group which allows for an accurate description of the critical regime as well as of correlation functions at finite momenta. The…
The functional flow equations for the Legendre effective action, with respect to changes in a smooth cutoff, are approximated by a derivative expansion; no other approximation is made. This results in a set of coupled non-linear…
Conformal prediction is an uncertainty quantification method that constructs a prediction set for a previously unseen datum, ensuring the true label is included with a predetermined coverage probability. Adaptive conformal prediction has…
We define a fixed point action in two-dimensional lattice ${\rm CP}^{N-1}$ models. The fixed point action is a classical perfect lattice action, which is expected to show strongly reduced cutoff effects in numerical simulations.…
For massless $\phi^4$ theory, we explicitly compute the lowest order non-local contributions to the one-loop effective action required for the determination of the trace anomaly. Imposing exact conformal invariance of the local part of the…
Recently, a new fractional derivative called the conformable fractional derivative is given which is based on the basic limit definition of the derivative in [1]. Then, the fractional versions of chain rules, exponential functions,…
We consider the problem of closeness of solutions of an exact and an averaged difference equations on an infinite interval. Appropriate assertions are derived from one special theorem on the stability under constantly acting perturbations.
The inversion theorem and convolution theorem of the conformable fractional Laplace transforms are developed. All the elementary properties of the classical Laplace transform are extended to the conformable fractional transform, and using…
We study exact renormalization group equations in the framework of the effective average action. We present analytical solutions for the scale dependence of the potential in a variety of models. These solutions display a rich spectrum of…
The generic structure of 4-point functions of fields residing in indecomposable representations of arbitrary rank is given. The presented algorithm is illustrated with some non-trivial examples and permutation symmetries are exploited to…
A geometric setup for constrained variational calculus is presented. The analysis deals with the study of the extremals of an action functional defined on piecewise differentiable curves, subject to differentiable, non-holonomic…
Well-founded fixed points have been used in several areas of knowledge representation and reasoning and to give semantics to logic programs involving negation. They are an important ingredient of approximation fixed point theory. We study…