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Numerical Polynomial Homotopy Continuation Method and String Vacua
Author
Source
Advances in High Energy Physics
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-10-23
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
Finding vacua for the four-dimensional effective theories for supergravity which descend from flux compactifications and analyzing them according to their stability is one of the central problems in string phenomenology.
Except for some simple toy models, it is, however, difficult to find all the vacua analytically.
Recently developed algorithmic methods based on symbolic computer algebra can be of great help in the more realistic models.
However, they suffer from serious algorithmic complexities and are limited to small system sizes.
In this paper, we review a numerical method called the numerical polynomial homotopy continuation (NPHC) method, first used in the areas of lattice field theories, which by construction finds all of the vacua of a given potential that is known to have only isolated solutions.
The NPHC method is known to suffer from no major algorithmic complexities and is embarrassingly parallelizable, and hence its applicability goes way beyond the existing symbolic methods.
We first solve a simple toy model as a warm-up example to demonstrate the NPHC method at work.
We then show that all the vacua of a more complicated model of a compactified M theory model, which has an SU(3) structure, can be obtained by using a desktop machine in just about an hour, a feat which was reported to be prohibitively difficult by the existing symbolic methods.
Finally, we compare the various technicalities between the two methods.
American Psychological Association (APA)
Mehta, Dhagash. 2011. Numerical Polynomial Homotopy Continuation Method and String Vacua. Advances in High Energy Physics،Vol. 2011, no. 2011, pp.1-15.
https://search.emarefa.net/detail/BIM-458596
Modern Language Association (MLA)
Mehta, Dhagash. Numerical Polynomial Homotopy Continuation Method and String Vacua. Advances in High Energy Physics No. 2011 (2011), pp.1-15.
https://search.emarefa.net/detail/BIM-458596
American Medical Association (AMA)
Mehta, Dhagash. Numerical Polynomial Homotopy Continuation Method and String Vacua. Advances in High Energy Physics. 2011. Vol. 2011, no. 2011, pp.1-15.
https://search.emarefa.net/detail/BIM-458596
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-458596