Related papers: Gradient Flows and the Curvature of Theory Space
Information theoretic geometry near critical points in classical and quantum systems is well understood for exactly solvable systems. Here we show that renormalization group flow equations can be used to construct the information metric and…
Every renormalization group flow in $d$ spacetime dimensions can be equivalently described as spectral deformations of a generalized free CFT in $(d-1)$ spacetime dimensions. This can be achieved by studying the effective action of the…
It has been suggested that higher-derivative gravity theories coupled to a scalar field with shift symmetry may be an important candidate for a quantum gravity. We show that this class of gravity theories are renormalizable in D = 3 and 4…
I give an overview over some work on rigorous renormalization theory based on the differential flow equations of the Wilson-Wegner renormalization group. I first consider massive Euclidean $\phi_4^4$-theory. The renormalization proofs are…
In this article we consider the length functional defined on the space of immersed planar curves. The $L^2(ds)$ Riemannian metric gives rise to the curve shortening flow as the gradient flow of the length functional. Motivated by the…
A higher-derivative, interacting, scalar field theory in curved spacetime with the most general action of sigma-model type is studied. The one-loop counterterms of the general theory are found. The renormalization group equations…
The flow equations of the Functional Renormalization Group are applied to the O(N)-symmetric scalar theory, for N=1 and N=4, in four Euclidean dimensions, d=4, to determine the effective potential and the renormalization function of the…
The holographic correspondence between 2d, N=2 quantum field theories and classical 4d, N=2 supergravity coupled to hypermultiplet matter is proposed. The geometrical constraints on the target space of the 4d, N=2 non-linear sigma-models in…
The field theoretic renormalization group is applied to the stochastic Navier-Stokes equation with the stirring force correlator of the form k^(4-d-2\epsilon) in the d-dimensional space, in connection with the problem of construction of the…
We put forward the first analysis of renormalization group flows in an area-metric theory, motivated by spin-foam quantum gravity. Area-metric gravity contains the well-known length-metric degrees of freedom of standard gravity as well as…
It is shown that the beta functions for four dimensional N=2 supersymmetric Yang-Mills theory without matter give integral curves on the moduli space some of which are geodesics of the natural metric on the moduli space. In particular the…
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…
Field theoretical renormalization group methods are applied to a simple model of a passive scalar quantity advected by the Gaussian non-solenoidal (``compressible'') velocity field with the covariance $\propto\delta(t-t')|…
Scalar field theory at finite temperature is investigated via an improved renormalization group prescription which provides an effective resummation over all possible non-overlapping higher loop graphs. Explicit analyses for the lambda…
We generalize the theory of gradient flows of semi-convex functions on CAT(0)-spaces, developed by Mayer and Ambrosio--Gigli--Savar\'e, to CAT(1)-spaces. The key tool is the so-called "commutativity" representing a Riemannian nature of the…
A general analysis of line defect renormalisation group (RG) flows in the $\varepsilon$ expansion below $d=4$ dimensions is undertaken. The defect beta function for general scalar-fermion bulk theories is computed to next-to-leading order…
Gradient descent-ascent (GDA) flows play a central role in finding saddle points of bivariate functionals, with applications in optimization, game theory, and robust control. While they are well-understood in Hilbert and Banach spaces via…
We compute the renormalization group flow of O(N) scalar field theories in de Sitter space using nonperturbative renormalization group techniques in the local potential approximation. We obtain the flow of the effective potential on…
Using double 2+2 and 3+1 nonholonomic fibrations on Lorentz manifolds, we extend the concept of W-entropy for gravitational fields in the general relativity, GR, theory. Such F- and W-functionals were introduced in the Ricci flow theory of…
The square-well fluid with hard-sphere diameters is studied within the framework of Thermodynamic Geometry (TG). Coexistence and spinodal curves, as well as the Widom line for ranges $\lambda^{*} = 1.25, 1.5, 2.0, 3.0$ for this fluid are…