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

Apr, 1997
38 pages
Published in:
  • Nucl.Phys.B 508 (1997) 147-180
e-Print:
Report number:
  • SLAC-PUB-7468,
  • IASSNS-HEP-97-28,
  • SNUTP-97-043,
  • SU-ITP-97-13

Citations per year

19972004201120182025051015
Abstract:
We study critical points of the BPS mass ZZ, the BPS string tension ZmZ_m, the black hole potential VV and the gauged central charge potential PP for M-theory compactified on Calabi-Yau three-folds. We first show that the stabilization equations for ZZ (determining the black hole entropy) take an extremely simple form in five dimensions as opposed to four dimensions. The stabilization equations for ZmZ_m are also very simple and determine the size of the infinite adS3adS_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 K\"ahler 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 VV and PP are continuous but not smooth across the flop transition, while ZZ and its first two derivatives, as well as ZmZ_m and its first derivative, are continuous. This in turn implies that supersymmetric stabilization of ZZ and ZmZ_m for a given configuration takes place in at most one point throughout the entire extended K\"ahler cone. The corresponding black holes (or string states) interpolate between different Calabi-Yau three-folds. At the boundaries of the extended K\"ahler cone we observe that electric states become massless and/or magnetic strings become tensionless.
Note:
  • 38 pages, LaTex, epsf, 8 figures (using 18.eps files), a version with figures of higher quality is available at http://www-leland.stanford.edu/~rahmfeld/5d.uu, typographical errors and one figure are corrected
  • 04.65.+e
  • 04.70.-s
  • 04.70.Dy
  • 68.35.Rh
  • field theory: M-theory
  • compactification
  • dimension: 5
  • field theory: soliton
  • string tension
  • critical phenomena