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

DOI10.1016/S0550-3213(97)00528-2zbMATH Open0925.81280arXivhep-th/9704142OpenAlexW2949733461MaRDI QIDQ1374318

Author name not available (Why is that?)

Publication date: 2 December 1997

Published in: (Search for Journal in Brave)

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

a d S_{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

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 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.

Full work available at URL: https://arxiv.org/abs/hep-th/9704142

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