相关论文: A Gradient Flow for Worldsheet Nonlinear Sigma Mod…

Renormalisation group flows of the bosonic nonlinear \sigma-model are governed, perturbatively, at different orders of \alpha', by the perturbatively evaluated \beta--functions. In regions where \frac{\alpha'}{R_c^2} << 1 the flow equations…

In this paper, it is elaborated the theory the Ricci flows for manifolds enabled with nonintegrable (nonholonomic) distributions defining nonlinear connection structures. Such manifolds provide a unified geometric arena for nonholonomic…

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 consider a normalization of the Ricci flow on a closed Riemannian manifold given by the evolution equation $\partial_{t}g(t)=-2(Ric(g(t))-\frac{1}{2\tau}g(t))$ where $\tau$ is a fixed positive number. Assuming that a solution for this…

In this paper, we holographically study the renormalization group (RG) flow in a three-dimensional Einstein-dilaton gravity with a potential permitting several types of the RG flow with nontrivial beta-functions. By using the intrinsic…

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…

In the first part of this short article, we define a renormalized F-functional for perturbations of non-compact steady Ricci solitons. This functional motivates a stability inequality which plays an important role in questions concerning…

We derive the renormalization group evolution of the quartic scalar theory with spontaneous symmetry breaking from an alternative flow equation, obtained within the externally sourced two-particle irreducible framework due to Garbrecht and…

We study the Renormalization Group (RG) flow of critical bosonic background fields in the framework of the RG approach to string theory. In this approach quantum field theory beta-functions are the extra inputs in solving the string theory…

A natural geometry, arising from the embedding into a Hilbert space of the parametrised probability measure for a given lattice model, is used to study the symmetry properties of real-space renormalisation group (RG) flow. In the projective…

We compute the one- and two-loop RG flow of integrable $\sigma$-models with Poisson-Lie symmetry. They are characterised by a twist function with $2N$ simple poles/zeros and a double pole at infinity. Hence, they capture many of the known…

Zamolodchikov's c-theorem type argument (and also string theory effective action constructions) imply that the RG flow in 2d sigma model should be gradient one to all loop orders. However, the monotonicity of the flow of the target-space…

We find the regime of our recently constructed topological nonrelativistic quantum gravity, in which Perelman's Ricci flow equations on Riemannian manifolds appear precisely as the localization equations in the path integral. In this…

This chapter describes how gradient flows and nonlinear power methods in Banach spaces can be used to solve nonlinear eigenvector-dependent eigenvalue problems, and how convergence of (discretized) approximations can be verified. We review…

The renormalization group flow in the theory space of a BRST invariant string $\sigma$-model is investigated. For the open bosonic string the non-perturbative off-shell effective action and its gauge symmetry properties are determined from…

We study two-dimensional spherical defects in d-dimensional Conformal Field Theories. We argue that the Renormalization Group (RG) flows on such defects admit the existence of a decreasing entropy function. At the fixed points of the flow,…

The a-function is a proposed quantity defined for quantum field theories which has a monotonic behaviour along renormalisation group flows, being related to the beta-functions via a gradient flow equation involving a positive definite…

Suppose $G$ is a compact Lie group, $H$ is a closed subgroup of $G$, and the homogeneous space $G/H$ is connected. The paper investigates the Ricci flow on a manifold $M$ diffeomorphic to $[0,1]\times G/H$. First, we prove a short-time…

We investigate the renormalization group (RG) structure of the gradient flow. Instead of using the original bare action to generate the flow, we propose to use the effective action at each flow time. We write down the basic equation for…

We investigate a new geometric flow which consists of a coupled system of the Ricci flow on a closed manifold M with the harmonic map flow of a map phi from M to some closed target manifold N with a (possibly time-dependent) positive…