The Implications of N =2 Supergravity Cosmology On the Topology of the Calabi-Yau Manifold

Document Type : Original Article

Authors

1 Department of Physics, Faculty of Science, Al-Azhar University, Cairo, Egypt.

2 Department of Physics, SUNY College at Cortland, Cortland, New York 13045, USA. University of Science and technology, Zewail City of Science and Technology, Giza 12578, Egypt.

Abstract

When N = 1 D = 11 supergravity is compactified on CY threefold to N = 2 D = 5 supergravity,  the action of the last is given in terms of the geometry of the CY manifold space, namely, in terms of the hypermultiplets. There are zi (i = 1,...,h2,1) complex structure moduli in the moduli space of the CY manifold which’s a special manifold with a metric . We solve the field equations of the complex structure moduli with the solution of the Einstein field equations to the moduli velocity norm   in the case of a 3- brane filled with radiation, dust, and energy embedded in the bulk of D = 5 supergravity. We get the time dependence of the moduli and the metric. Then we can further deduce the geometry of the moduli space by getting the  potential that  directly relates to the volume of the CY manifold.

Keywords

Main Subjects

References

[1]       Douglas Michael R. Calabi-Yau metrics and string compactification. Nucl. Phys. B. 2015; 898: 667.
[2]      Green Brain R. String theory on Calabi-Yau manifolds. Theoretical Advanced Study Institute in Elementary Particle Physics ( TASI 96 ). 1996: 543.
[3]      Candelas Philip, De la Ossa Xenia.  Moduli space of Calabi-Yau manifolds.  XIII International School of Theoretical Physics: The Standard Model and Beyond. 1989.
[4]       Emam Moataz H.  The many symmetries of Calabi-Yau compactification. Class. Quant. Grav. 2010; 27: 163001.
[5]      Candelas Philip, De la Ossa Xeni,  Green Paul S,  Parkes Linda. A Pair of Calabi-Yau manifolds as an exactly soluble superconformal field theory.  Nucl. Phys. B. 1991; 359: 2174.
[6]       Berglund P,  Candelas P, De la Ossa X,  Font A,  Huebsch T,  Jancic D,  Quevedo F. Periods for Calabi-Yau and Landau-Ginzburg vacua.  Nucl. Phys. B; 1991; 355: 455.
[7]      Aleshkin Konstantin, Belavin Alexander. A new approach for computing the geometry of the moduli spaces for a Calabi-Yau manifold. J. Phys. A. 2018;  51 (5): 05540.
[8]      Aleshkin Konstantin, Belavin Alexander. Special geometry on the 101 dimesional moduli space of the quintic threefold. JHEP. 2018; 1803: 018.
[9]      Emam Moataz H,  Salah HH,  Salem Safinaz. Brane-worlds and the Calabi – Yau complex structure moduli. Class. Quant. Grav. 2020; 37 (19 ): 195007.
[10] Emam Moataz H. BPS brane cosmology in N = 2 supergravity.  Class. Quant. Grav. 2015; 32 (18) :185014.

Files

Share

How to cite

Statistics