The normalized second order renormalization group flow on closed surfaces

TL;DR

This paper investigates a normalized second order renormalization group flow on closed surfaces, analyzing its properties and deriving formulas, especially for surfaces with zero or positive Euler characteristic.

Contribution

It introduces and studies a normalized second order RG flow on closed surfaces, providing foundational properties and formulas for specific topological cases.

Findings

Flow properties analyzed for zero Euler characteristic surfaces

Formulas established for positive Euler characteristic surfaces

General properties of the flow discussed

Abstract

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 and positive Euler characteristic.