El flujo RG-2, cotas para los escalares de curvatura

Abstract

On this work we present some results about the second order renormalization group flow of the non-linear Sigma Model of String Theory, the RG-2 flow. We calculate the evolution, under the RG-2 flow, of the the Riemann curvature tensor and the Kretschmann scalar. The solutions are governed by reaction-diffusion type equations, then we introduce a maximun principle theorem and use it to prove that, under certain conditions, it is possible to constrain the curvature of the flow solutions, at least for a short period of time. Our theoretical results, when applied to constant sectional curvature geometries, reproduce the expected results . Finally we present a brief analysis of the behavior of scalar curvature and Hamilton entropy under RG-2 flow.