Comments on D branes and the renormalization group

TL;DR

This paper reviews the holographic renormalization group formalism for Dp branes, relating bulk-boundary correspondence, and discusses implications for brane cosmology and the Randall-Sundrum scenario.

Contribution

It connects the de Boer-Verlinde-Verlinde formalism to Dp brane vacua and explores the gravitational coupling and beta function in this context.

Findings

Gravitational coupling on the Dp brane is proportional to the Yang-Mills c-function.

Beta function flow matches classical expectations.

Proposes a mechanism for brane cosmology dynamics.

Abstract

We review the de Boer-Verlinde-Verlinde formalism for the renormalization group in the context of Dp brane vacua. We comment on various aspects of the dictionary between bulk and boundary and relate the discussion to the Randall-Sundrum scenario. We find that the gravitational coupling for the Randall-Sundrum gravity on the Dp brane worldvolume is proportional to the c-function of the Yang-Mills theory. We compute the beta function and find the expected uneventful flow prescribed by the classical dimension of the Yang-Mills operator. Finally, we argue for a dynamical mechanism for determining the cosmology on the brane.