The perturbative Ricci flow in gravity

arXiv (Cornell University)

Abstract

We develop a perturbative formulation of the Ricci flow in gravity. Following steps analogous to the gradient flow in QCD, we supplement the usual Feynman rules for perturbative gravity by flowed propagators and vertices as well as graviton flow lines which describe the evolution of gravity along the Ricci flow. By calculating vacuum expectation values of a number of independent operators at the two-loop level, we derive the required counterterms of the flowed action. Our results allow us to define a Ricci-flow based renormalization scheme for Newton's constant $G_N$. Studying its renormalization group behavior, we recover a non-Gaußian fixed point in accordance with well-known non-perturbative considerations

Authors 4

1. Robert V. Harlander Aachen

   RWTH Aachen University

   Affiliation as printed

   TTK , RWTH Aachen University , 52067 Aachen , Germany

2. Yannick Kluth

   University of Toronto

   Affiliation as printed

   Department of Physics , University of Toronto , ON M5S 1A7 , Canada

3. Jonas T. Kohnen Aachen

   RWTH Aachen University

   Affiliation as printed

   TTK , RWTH Aachen University , 52067 Aachen , Germany

4. Henry Werthenbach Aachen

   RWTH Aachen University

   Affiliation as printed

   TTK , RWTH Aachen University , 52067 Aachen , Germany