Physics Commons^™

The Toric Approach To F-Theory Model Building, Herbie L. Smith

Honors Theses and Capstones

We describe the theoretical motivation for F-theory as a non-perturbative generalization of string theory. The four complex-dimensional compactification spaces of F-theory, called elliptically-fibered Calabi-Yau manifolds, consist of the six compact dimensions of string theory, plus a two-dimensional fiber that describes the string coupling field as a function of position on the string theory manifold. The methods of toric geometry are developed and applied to construct examples of elliptically-fibered Calabi-Yau manifolds. We analyze in detail models in which the fiber is free of singularities as a test bed for a more general analysis.

Ads/Cft In String Theory And M-Theory, Daniel R. Gulotta '03

Doctoral Dissertations

The AdS/CFT correspondence is a powerful tool that can help shed light on the relationship between geometry and field theory.

The first part of this thesis will focus on the construction of theories dual to Type IIB string theory on AdS₅ x Y⁵, where Y⁵ is a toric Sasaki-Einstein manifold. This thesis will introduce a consistency condition called "proper ordering" and demonstrate that it is equivalent to several other previously known consistency conditions. It will then give an efficient algorithm that produces a consistent field theory for any toric Sasaki-Einstein Y⁵.

The second part …

Gauge-Gravity Duality And Its Applications To Cosmology And Fluid Dynamics, Jae-Hyuk Oh

University of Kentucky Doctoral Dissertations

This thesis is devoted to the study of two important applications of gauge-gravity duality: the cosmological singularity problem and conformal fluid dynamics. Gauge-gravity duality is a concrete dual relationship between a gauge theory (such as electromagnetism, the theories of weak and strong interactions), and a theory of strings which contains gravity. The most concrete application of this duality is the AdS/CFT correspondence, where the theory containing gravity lives in the bulk of an asymptotically anti-de-Sitter space-time, while the dual gauge theory is a deformation of a conformal field theory which lives on the boundary of anti-de-Sitter space-time(AdS).

Our first application …