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Black hole condensation and the web of Calabi-Yau manifolds. (English) Zbl 0908.32006
Summary: We review recent work concerning topology changing phase transitions through black hole condensation in Type II string theory. We then also briefly describe a present study aimed at extending the known web of interconnections between Calabi-Yau manifolds. We show, for instance, that all 7555 Calabi-Yau hypersurfaces in weighted projective four space are mathematically connected by extremal transitions.

##### MSC:
 32G81 Applications of deformations of analytic structures to the sciences 14J32 Calabi-Yau manifolds (algebro-geometric aspects) 83C57 Black holes
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##### References:
 [1] Witten, E.: Phases of N=2 theories in two dimensions. Nucl. phys. 403, 159 (1993) · Zbl 0910.14020 [2] Aspinwall, P.; Greene, B.; Morrison, D.: Calabi-Yau moduli space, mirror manifolds, and spacetime topology change in string theory. Nucl. phys. 416, 414 (1994) · Zbl 0899.32006 [3] Strominger, A.: Massless black holes and conifolds in string theory. Nucl. phys. 451, 96 (1995) · Zbl 0925.83071 [4] Greene, B. R.; Morrison, D. R.; Strominger, A.: Black hole condenstaion and the unification of sting vacua. Nucl. phys. 451, 109 (1995) · Zbl 0908.53041 [5] N. Seiberg and E. Witten, Electric-Magnetic Duality, Monopole Condensation, and Confinement in N = 2 Supersymmetric Yang-Mills Theory, Nucl. Phys. B426 19 · Zbl 0996.81510 [6] Bershadski, M.; Sadov, V.; Vafa, C.: D-strings on D-manifolds · Zbl 1004.81535 [7] Horowitz, G.; Strominger, A.: Black strings and p-branes. Nucl. phys. 368, 444-462 (1992) [8] Ceresole, A.; D’auria, R.; Ferrara, S.; Van Proeyen, A.: Duality transformations in supersymmetric Yang-Mills theory coupled to supergravity. Nucl. phys. 444, 92 (1995) · Zbl 0990.81736 [9] Lefshetz, S.: L’analysis situs et la géométrie algébraique. 1924Gautier-villarsberlinselected papers, 283-439 (1924) [10] Clemens, H.: Double solids. Advances in mathematics 47, 107-230 (1983) · Zbl 0509.14045 [11] Candelas, P.; Green, P. S.; Hübsch, T.: Rolling among Calabi-Yau vacua. Nucl. phys. 330, 49 (1990) · Zbl 0985.32502 [12] Gepner, D.: Exactly solvable string compactificatios on manifolds of $$SU(N)$$ holonomy. Phys. lett. 199B, 380 (1987) [13] Candelas, P.; Lynker, M.; Schimmrigk, R.: Calabi-Yau manifolds in weighted $$\mathbb{P}$$4. Nucl. phys. 341, 383 (1990) · Zbl 0962.14029 [14] Kreuzer, M.; Skarke, H.: No mirror symmetry in Landau-Ginsburg spectra. Nucl. phys. 388, 113 (1992) [15] Batyrev, V.; Borisov, L. A.: On Calabi-Yau complete intersections in toric varieties · Zbl 0908.14015 [16] P. Candelas, private communication. [17] Argyres, P.; Douglas, M.: New phenomena in $$SU(3)$$ supersymmetric gauge theory. Nucl. phys. 448, 93 (1995) · Zbl 1009.81572 [18] Morrison, D. R.: Through the looking Glass. Lecture at CIRM conference (June, 1994) · Zbl 0935.32020 [19] Fulton, W.: Introduction to toric varieties. Annals of math. Studies 131 (1993) · Zbl 0813.14039 [20] Batyrev, V.: Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties. J. alg. Geom. 3, 493 (1994) · Zbl 0829.14023 [21] Hayakawa, Y.: Degeneration of Calabi-Yau manifold with Weil-Petersson metric [22] Aspinwall, P. S.; Greene, B. R.; Morrison, D. R.: The monomial-divisor mirror map. Internat. math. Res. notices, 319 (1993) · Zbl 0798.14030 [23] A. M. Gabrielov, Intersection Matrixes for Certain Singularities, Functional Analysis and its Applications, vol. 7 No. 3 pp. 18–32 [24] Witten, E.: Some comments on string dynamics · Zbl 1003.81535
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