Critical points and phase transitions in 5d compactifications of M-theory

Abstract

We study critical points of the BPS mass Z , the BPS string tension Z m , the black hole potential V and the gauged central charge potential P for M-theory compactified on Calabi-Yau three-folds. We first show that the stabilization equations for Z (determining the black hole entropy) take an extremely simple form in five dimensions as opposed to four dimensions. The stabilization equations for Z m are also very simple and determine the size of the infinite adS 3 throat of the string. The black hole potential in general exhibits two classes of critical points: supersymmetric critical points which coincide with those of the central charge and non-supersymmetric critical points. We then generalize the discussion to the entire extended Kähler cone encompassing topologically different but birationally equivalent Calabi-Yau three-folds that are connected via flop transitions. We examine behavior of the four potentials to probe the nature of these phase transitions. We find that V and P are continuous but not smooth across the flop transition, while Z and its first two derivatives, as well as Z m and its first derivative, are continuous. This in turn implies that supersymmetric stabilization of Z and Z m for a given configuration takes place in at most one point throughout the entire extended Kähler cone. The corresponding black holes (or string states) interpolate between different Calabi-Yau three-folds. At the boundaries of the extended Kähler cone we observe that electric states become massless and/or magnetic strings become tensionless.