Instabilities of near-extremal smeared branes and the correlated stability conjecture

We consider the classical and local thermodynamic stability of non- andnear-extremal Dp-branes smeared on a transverse direction. These two types ofstability are connected through the correlated stability conjecture for whichwe give a proof in this specific class of branes. The proof is analogous tothat of Reall for unsmeared branes, and includes the construction of anappropriate two-parameter off-shell family of smeared Dp-brane backgrounds. Weuse the boost/U-duality map from neutral black strings to smeared black branesto explicitly demonstrate that non-and near-extremal smeared branes areclassically unstable, confirming the validity of the conjecture. Fornear-extremal smeared branes in particular, we show that a natural definitionof the grand canonical ensemble exists in which these branes arethermodynamically unstable, in accord with the conjecture. Moreover, we examinethe connection between the unstable Gregory-Laflamme mode of charged branes andthe marginal modes of extremal branes. Some features of T-duality andimplications for the finite temperature dual gauge theories are also discussed.Comment: 35 pages, 1 figur