Toric Elliptic Fibrations Over Hirzebruchs / Prashant Subbarao.

Format:

Book

Manuscript

Thesis/Dissertation

Author/Creator:

Subbarao, Prashant, author.

Contributor:

Donagi, Ron, degree supervisor.

Block, Jonathan L., degree committee member.

Mele, E. J. (Eugene J.), degree committee member.

Sheth, Ravi K., degree committee member.

Thomson, Evelyn J., degree committee member.

University of Pennsylvania. Department of Physics and Astronomy, degree granting institution.

Language:

English

Subjects (All):

Penn dissertations--Physics and Astronomy.

Physics and Astronomy--Penn dissertations.

Local Subjects:

Penn dissertations--Physics and Astronomy.

Physics and Astronomy--Penn dissertations.

Physical Description:

xiv, 136 leaves : illustrations ; 29 cm

Production:

[Philadelphia, Pennsylvania] : University of Pennsylvania, 2017.

Summary:

F-theory offers a compelling, nonperturbative framework in which to construct string vacua in even dimensional space-time. These theories are described by an elliptically fibered Calabi-Yau manifold over a base of complex dimension d for a low energy theory in 10--2d dimensional space-time. The structure of the gauge group in the low-energy theory is captured principally in the singularities of the elliptic fibration. In the parlance of type IIB string theory, the gauge group is reflected in 7-branes which wrap on topologically nontrivial cycles of the base manifold.The geometry of the gauge groups and matter representations that arise in F-theory has been worked out by Taylor-Morrison. While there is a finite set of gauge groups and matter content that arise in F-theory constructions of 6D supergravity theories, a given base may yield a wide range of both. Models that have different spectra over a common F-theory base can be configured by tuning the coefficients in the Weierstrass description of the model such that certain codimension-one and -two singularities materialize in the elliptic fibration. As the structure of singularities in the fibration becomes more sophisticated, the accompanying matter representations become more exotic.Taylor-Morrison systematically classified the smooth toric bases that support elliptically fibered Calabi-Yau threefolds. By analyzing the intersection structure of irreducible effective divisors on the base, they found that there are 61,539 distinct toric bases. Many Calabi-Yau manifolds can be realized as hypersurfaces in toric varieties of one higher dimension which, following Batyrev, can be constructed with reflexive polyhedra. Kreuzer-Skarke systematically identified the 473,800,776 reflexive polytopes in 4D. This suggests another approach to understanding elliptically fibered Calabi-Yau threefolds for 6D theories: by analyzing polytopes in 4D, one can understand all toric elliptic fibrations for F-theory from this list. Braun identified the polytopes corresponding to elliptic fibrations over base CP2 .In this thesis, I systematically identify the polytopes that correspond to elliptic fibrations of the first Hirzebruch surfaces F 1 as well as F12, the final Hirzebruch surface admitted in an F-Theoretic context. I study the hodge structure of all admitted 4D polytopes; as well as the Gauge groups and Kodaira fibers.

Notes:

Ph. D. University of Pennsylvania 2017.

Department: Physics and Astronomy.

Supervisor: Ron Y. Donagi.

Includes bibliographical references.

OCLC:

1334945231