Second Order Renormalization Group Flow on Warped Product Manifolds

Year 2019, Volume: 16 Issue: 1, 81 - 97, 31.05.2019

Asadollah Razavi Zoheir Toeiserkani

Abstract

In this work we have studied the evolution of a warped product (WP) manifold under second order
renormalization group (RG-2) flow. We have shown some conditions for the existence of a solution of RG-2
flow on WP manifolds. Also, we have found a necessary condition for warped function under RG-2 flow. In
particular, we study some special WP metric of real line with a manifold. Eventually, by extending conditions
to pseudo-Riemannian manifold, we find a PDE for Robertson-Walker (RW) metrics, and show that there is
no RG-2 flow for RW metrics.

Keywords

Ricci flow, second order renormalization group flow, warped product manifold

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