相关论文: Irreversibility of World-sheet Renormalization Gro…

The renormalization group flow in two-dimensional field theories that are coupled to gravity has unusual features: First, the flow equations are second order in derivatives. Second, in the presence of handles the flow has quantum mechanical…

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…

In this letter we study renormalization group (RG) flows between 2d conformal field theories enjoying extended higher-spin $\mathcal{W}$-symmetry. We propose a new class of RG flows between the diagonal minimal models of…

The quantum field theory of two-dimensional sigma models with bulk and boundary couplings provides a natural framework to realize and unite different species of geometric flows that are of current interest in mathematics. In particular, the…

We study the Ricci flow on $\mathbb{R}^{n+1}$, with $n\geq 2$, starting at some complete bounded curvature rotationally symmetric metric $g_{0}$. We first focus on the case where $(\mathbb{R}^{n+1},g_{0})$ does not contain minimal…

Let $(\mathcal{M},g)$ be a closed Riemannian manifold. The $\textit{ second order approximation}$ to the perturbative renormalization group flow for the nonlinear sigma model (RG-2 flow) is given by : \[ \frac{\partial }{\partial t} \, g(t)…

We discuss from a geometric point of view the connection between the renormalization group flow for non--linear sigma models and the Ricci flow. This offers new perspectives in providing a geometrical landscape for 2D quantum field…

We present a proof of the irreversibility of renormalization group flows, i.e. the c-theorem for unitary, renormalizable theories in four (or generally even) dimensions. Using Ward identities for scale transformations and spectral…

A renormalization group study of a scalar theory coupled to gravity through a general functional dependence on the Ricci scalar in the action is discussed. A set of non-perturbative flow equations governing the evolution of the new…

We consider a closed manifold M with a Riemannian metric g(t) evolving in direction -2S(t) where S(t) is a symmetric two-tensor on (M,g(t)). We prove that if S satisfies a certain tensor inequality, then one can construct a forwards and a…

We present a monotonic expression for the Ricci flow, valid in all dimensions and without curvature assumptions. It is interpreted as an entropy for a certain canonical ensemble. Several geometric applications are given. In particular, (1)…

We develop a perturbative formulation of the Ricci flow in gravity. Following steps analogous to the gradient flow in QCD, we supplement the usual Feynman rules for perturbative gravity by flowed propagators and vertices as well as graviton…

In this paper, we study curvature behavior at the first singular time of solution to the Ricci flow on a smooth, compact n-dimensional Riemannian manifold $M$, $\frac{\partial}{\partial t}g_{ij} = -2R_{ij}$ for $t\in [0,T)$. If the flow has…

Implementing the Wilsonian renormalization group (RG) transformation in a nonperturbative way, we construct an effective holographic dual description with an emergent extradimension identified with an RG scale. Taking the large$-N$ limit,…

We present a nonperturbative renormalization group solution of the Gell-Mann--Levy $\sigma$-model which was originally proposed as a phenomenological description of the dynamics of nucleons and mesons. In our version of the model the…

We study inflation as a "cosmic" renormalization-group flow. The flow, which encodes the dependence on the background metric, is described by a running coupling $\alpha $, which parametrizes the slow roll, a de Sitter free, analytic beta…

We demonstrate that the reformulation of renormalization group (RG) flow equations as non-linear heat equations has severe implications on the understanding of RG flows in general. We demonstrate by explicitly constructing an entropy…

We extend the Wilson renormalization group (RG) to supersymmetric theories. As this regularization scheme preserves supersymmetry, we exploit the superspace technique. To set up the formalism we first derive the RG flow for the massless…

Motivated by the renormalization group (RG) approach to $c=0$ matrix model of Bre\'zin and Zinn-Justin, we develop a RG scheme for $c=1$ matrix model on a circle and analyze how the two coupling constants in double scaling limit with…

We analyze the behaviour of heterotic squashed-Wess-Zumino-Witten backgrounds under renormalization-group flow. The flows we consider are driven by perturbation creating extra gauge fluxes. We show how the conformal point acts as an…