CRITICAL-POINTS AND PHASE-TRANSITIONS IN 5D COMPACTIFICATIONS OF M-THEORY

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 t hat the stabilization equations for Z (determining the black hole entr opy) take an extremely simple form in five dimensions as opposed to fo ur dimensions. The stabilization equations for Z(m) are also very simp le and determine the size of the infinite adS(3)throat of the string. The black hole potential in general exhibits two classes of critical p oints: supersymmetric critical points which coincide with those of the central charge and non-supersymmetric critical points. We then genera lize the discussion to the entire extended Kahler cone encompassing to pologically different but birationally equivalent Calabi-Yau three-fol ds that are connected via flop transitions, We examine behavior of the four potentials to probe the nature of these phase transitions. We fi nd that V and P are continuous but not smooth across the flop transiti on, while Z and its first two derivatives, as well as Z(m) and its fir st derivative, are continuous. This in turn implies that supersymmetri c stabilization of Z and Z(m) for a given configuration takes place in at most one point throughout the entire extended Kahler cone, The cor responding black holes (or string states) interpolate between differen t Calabi-Yau three-folds. At the boundaries of the extended Kahler con e we observe that electric states become massless and/or magnetic stri ngs become tensionless. (C) 1997 Elsevier Science B.V.