Related papers: Convergence and stability of the renormalisation g…
We study the convergence of the derivative expansion for flow equations. The convergence strongly depends on the choice for the infrared regularisation. Based on the structure of the flow, we explain why optimised regulators lead to better…
We revisit optimization of functional renormalization group flows by analyzing regularized loop integrals. This leads us to a principle, the Principle of Strongest Singularity, and a corresponding order relation which allows to order…
We consider some applications of the Renormalization Group flow equations obtained by resorting to a specific class of proper time regulators. Within this class a particular limit that corresponds to a sharpening of the effective width of…
I am showing how the ideas behind the renormalisation group can be generalised in order to produce the desired reduction in the degrees of freedom other that the ones considered up to now. Instead of looking only at the renormalisation…
We discuss the following proposition: Renormalization Group flow of quantum theory with a biased symmetry exhibits a fixed hypersurface at which the symmetry is exact. Such emergent symmetries may have important phenomenological…
We discuss structural aspects of the functional renormalisation group. Flows for a general class of correlation functions are derived, and it is shown how symmetry relations of the underlying theory are lifted to the regularised theory. A…
Working with scalar field theories, we discuss choices of regulator that, inserted in the functional renormalization group equation, reproduce the results of dimensional regularization at one and two loops. The resulting flow equations can…
We study a proper-time renormalisation group, which is based on an operator cut-off regularisation of the one-loop effective action. The predictive power of this approach is constrained because the flow is not an exact one. We compare it to…
The renormalization group flow in a general renormalizable gauge theory with a simple gauge group in 3+1 dimensions is analyzed. The flow of the ratios of the Yukawa couplings and the gauge coupling is described in terms of a bounded…
We study exact renormalisation group flows for background field dependent regularisations. It is shown that proper-time flows are approximations to exact background field flows for a specific class of regulators. We clarify the role of the…
We explore the regime of ``superfast'' reactivity that has been predicted to occur in turbulent flow in the presence of potential disorder. Computer simulation studies confirm qualitative features of the previous renormalization group…
A recently proposed renormalization group technique, based on the hierarchical structures present in theories with fluctuating geometry, is implemented in the model of branched polymers. The renormalization group equations can be solved…
The dependence of function renormalization group equation on regulators is investigated. A parameter is introduced to control the suppression of regulators. Functional renormalization group equations will become regulator-independent if…
Within the exact renormalisation group, the scaling solutions for O(N) symmetric scalar field theories are studied to leading order in the derivative expansion. The Gaussian fixed point is examined for d>2 dimensions and arbitrary infrared…
We prove the stability of the torus, and with suitable rescaling, hyperbolic space under the (two-loop) renormalization group flow for the nonlinear sigma model. To prove stability we use similar techniques to \cite{GIK02}, where the…
Renormalization group theory is a powerful and intriguing technique with a wide range of applications. One of the main successes of renormalization group theory is the description of continuous phase transitions and the development of…
Large-$N$ renormalization group equations for one- and two-matrix models are derived. The exact renormalization group equation involving infinitely many induced interactions can be rewritten in a form that has a finite number of coupling…
We propose that the broad architecture of the renormalization group flow in quantum field theories is, at least in part, fixed by unitarity. The precise statement is summarized in the Unitarity Flow Conjecture, which states that the…
We study the optimisation of exact renormalisation group (ERG) flows. We explain why the convergence of approximate solutions towards the physical theory is optimised by appropriate choices of the regularisation. We consider specific…
Functional renormalisation group approach is applied to a system of kaons with finite chemical potential. A set of approximate flow equations for the effective couplings is derived and solved. At high scale the system is found to be at the…