Instabilities of Near-Extremal Smeared Branes and the Correlated Stability Conjecture

TL;DR

This paper proves the correlated stability conjecture for smeared Dp-branes, demonstrating their classical and thermodynamic instabilities, and explores the implications for gauge theories and dualities.

Contribution

It provides a proof of the correlated stability conjecture for smeared Dp-branes and connects classical instabilities with thermodynamic properties.

Findings

Non- and near-extremal smeared branes are classically unstable.

Near-extremal smeared branes are thermodynamically unstable in a suitable ensemble.

The Gregory-Laflamme instability relates to extremal brane modes.

Abstract

We consider the classical and local thermodynamic stability of non- and near-extremal Dp-branes smeared on a transverse direction. These two types of stability are connected through the correlated stability conjecture for which we give a proof in this specific class of branes. The proof is analogous to that of Reall for unsmeared branes, and includes the construction of an appropriate two-parameter off-shell family of smeared Dp-brane backgrounds. We use the boost/U-duality map from neutral black strings to smeared black branes to explicitly demonstrate that non-and near-extremal smeared branes are classically unstable, confirming the validity of the conjecture. For near-extremal smeared branes in particular, we show that a natural definition of the grand canonical ensemble exists in which these branes are thermodynamically unstable, in accord with the conjecture. Moreover, we examine the connection between the unstable Gregory-Laflamme mode of charged branes and the marginal modes of extremal branes. Some features of T-duality and implications for the finite temperature dual gauge theories are also discussed.