# Metric for gradient renormalization group flow of the worldsheet sigma model beyond first order

@article{Oliynyk2007MetricFG, title={Metric for gradient renormalization group flow of the worldsheet sigma model beyond first order}, author={Todd A. Oliynyk and Vardarajan Suneeta and Eric Woolgar}, journal={Physical Review D}, year={2007}, volume={76}, pages={045001} }

Tseytlin has recently proposed that an action functional exists whose gradient generates to all orders in perturbation theory the Renormalization Group (RG) flow of the target space metric in the worldsheet sigma model. The gradient is defined with respect to a metric on the space of coupling constants which is explicitly known only to leading order in perturbation theory, but at that order is positive semi-definite, as follows from Perelman’s work on the Ricci flow. This gives rise to a…

## 15 Citations

### THE CIGAR SOLITON AND THE RICCI FLOWS PERTURBATION SOLUTIONS IN THE TWO-DIMENSIONAL STRING σ MODEL

- Physics
- 2023

The Ricci ﬂows perturbation equations and the Weyl anomaly coeﬃcients are derived in the two-dimensional bosonic string σ model. These equations correspond to the two-loop ﬂow equations for the…

### Energy, entropy and the Ricci flow

- Mathematics
- 2008

The Ricci flow (RF) is a heat equation for metrics, which has recently been used to study the topology of closed three-manifolds. In this paper we apply Ricci flow techniques to general relativity.…

### BF-like symmetries for general relativity and Ricci flows on the space of connections

- Mathematics
- 2009

Using a first-order formulation for general relativity that assumes the independence between the metric and the connection of the background manifold, it is proved that new gauge symmetries of the…

### Gravity localization in a string-cigar braneworld

- Physics
- 2012

We proposed a six-dimensional string-like braneworld built from a warped product between a 3-brane and the Hamilton cigar soliton space, the string-cigar braneworld. This transverse manifold is a…

### Stability of the (Two-Loop) Renormalization Group Flow for Nonlinear Sigma Models

- Mathematics
- 2008

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…

### Some Applications of Ricci Flow in Physics

- Physics
- 2007

I discuss certain applications of the Ricci flow in physics. I first review how it arises in the renormalization group (RG) flow of a nonlinear sigma model. I then review the concept of a Ricci…

### On new traveling wave solutions and conserved densities for the 2D Ricci flow model

- Mathematics
- 2019

In this paper some travelling wave solutions and conservation laws for the 2D Ricci flow model in conformal gauge are investigated. A guideline able to classify the types of solutions according to…

### Mean curvature flow on Ricci solitons

- Mathematics
- 2009

We study monotonic quantities in the context of combined geometric flows. In particular, focusing on Ricci solitons as the ambient space, we consider solutions of the heat-type equation integrated…

### Higher order geometric flows on three-dimensional locally homogeneous spaces

- Mathematics
- 2013

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 wherever possible,…

## 34 References

### Sigma model renormalization group flow, ``central charge'' action, and Perelman's entropy

- Mathematics
- 2007

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

### Weyl consistency conditions and a local renormalisation group equation for general renormalisable field theories

- Mathematics, Physics
- 1991