Related papers: Renormalization Group and the Ricci flow
This paper studies the normalized Ricci flow on surfaces with conical singularities. It's proved that the normalized Ricci flow has a solution for a short time for initial metrics with conical singularities. Moreover, the solution makes…
A study of the renormalization group flow in the three-dimensional nonlinear O(N) sigma model using Monte Carlo Renormalization Group (MCRG) techniques is presented. To achieve this, we combine an improved blockspin transformation with the…
We study the renormalization group flow of the O(N) non-linear sigma model in arbitrary dimensions. The effective action of the model is truncated to fourth order in the derivative expansion and the flow is obtained by combining the…
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…
Within the exact renormalisation group approach, it is shown that stability properties of the flow are controlled by the choice for the regulator. Equally, the convergence of the flow is enhanced for specific optimised choices for the…
We study the non-perturbative renormalization group flow of the nonlinear O(N) sigma model in two and three spacetime dimensions using a scheme that combines an effective local Hybrid Monte Carlo update routine, blockspin transformations…
We give a global picture of the Ricci flow on the space of three-dimensional, unimodular, nonabelian metric Lie algebras considered up to isometry and scaling. The Ricci flow is viewed as a two-dimensional dynamical system for the evolution…
We analyse second order (in Riemann curvature) geometric flows (un-normalised) on locally homogeneous three manifolds and look for specific features through the solutions (analytic whereever possible, otherwise numerical) of the evolution…
In this work we study renormalization-group flows by deforming a class of conformal sigma-models. At leading order in $\alpha'$, renormalization-group equations represent a Ricci flow. In the three-sphere background, the latter is described…
We implement an explicit two-loop calculation of the coupling functions and the self-energy of interacting fermions with a two-dimensional flat Fermi surface in the framework of the field theoretical renormalization group (RG) approach.…
The target space of the non-linear $\sigma$-model is a Riemannian manifold. Although it can be any Riemannian metric, there are certain physically interesting geometries which are worth to study. Here, we numerically evolve the…
We demonstrate the irreversibility of a wide class of world-sheet renormalization group (RG) flows to first order in $\alpha'$ in string theory. Our techniques draw on the mathematics of Ricci flows, adapted to asymptotically flat target…
We construct a zero-curvature representation for a four-parameter family of non-linear sigma models with a Kalb-Ramond term. The one-loop renormalization is performed that gives rise to a new set of ancient and eternal solutions to the…
We study a normalized version of the second order renormalization group flow on closed Riemannian surfaces. We discuss some general properties of this flow and establish several basic formulas. In particular, we focus on surfaces with zero…
We review the rigorous work on many Fermions models which lead to the first constructions of interacting Fermi liquids in two dimensions, and allowed to prove that there are different scaling regimes in two dimensions, depending on the…
We present in this paper a general approach to study the Ricci flow on homogeneous manifolds. Our main tool is a dynamical system defined on a subset H(q,n) of the variety of (q+n)-dimensional Lie algebras, parameterizing the space of all…
The two-loop renormalization group flow is studied via the induced bracket flow on 3D unimodular Lie groups. A number of steady solitons are found. Some of these steady solitons come from maximally symmetric metrics that are steady,…
We analyze the Ricci flow of a noncompact metric that describes a two-dimensional black hole. We consider entanglement entropy of a 2d black hole which is due to the quantum correlations between two subsystems: one is inside and the other…
We discuss some higher-loop studies of renormalization-group flows and fixed points in various quantum field theories.
In previous work, Angenent, Isenberg, and Knopf created type-II Ricci flow neckpinch singularities. In this paper we construct solutions to Ricci flow whose initial data is the singular metric resulting from these singularities. We show in…