Introduction Modern Physics Two regimes: general relativity for large scale phenomena and quantum mechanics for small scale phenomena Regimes cannot be mixed String Theory Fundamental theory of physics Describes both cosmology and particle physics Requires ten dimensions Six dimensions are compactified Extra Dimensions Compactify on Calabi-Yau manifolds [1]. Shape and size of a Calabi-Yau effect string interactions and the evolving universe. Potential energy of the universe depends on volume and shape of Calabi-Yau, with shape fixed by generalized magnetic fluxes. Potential energy determines the early universe, inflation, current accelerated expansion, and fate of the universe. Figure 1: Projection of a Calabi-Yau manifold. Swiss Cheese Example. The volume for a model with two Kahler moduli, t i : Define four-cycles, τ i, as derivatives of volume with respect to two-cycles: Model is Swiss Cheese if there exists a basis of four-cycles that can be written as a perfect square in terms of two-cycles. In this case: Future Work – Physical Implications Study cosmology of Swiss Cheese Calabi-Yau manifolds Study particle physics from embedded del Pezzo content Attempt to identify models with cosmology and particle physics that resemble our universe Journal article outlining findings to appear Ongoing Research Swiss Cheese Search Extending search for Swiss Cheese manifolds. New models: more Kahler moduli, non-simplicial Making the search comprehensive Higher Dimensions Extension to higher dimensions Applications to F-Theory—contains two additional auxiliary dimensions Figure 2: Illustration of D-branes confined to a singularity in a Calabi-Yau caused by a collapsing del Pezzo divisor. References 1) B. Greene. String Theory on Calabi-Yau Manifolds. Proceedings TASI-96, World Scientific (1997). 2) V. Balasubramanian, P. Berglund, J. P. Conlon, F. Quevedo. Systematics of Moduli Stabilisation in Calabi-Yau Flux Compactifications. JHEP 0503 (2005) ) M. Kreuzer, H. Skarke. Complete Classification of Reflexive Polyhedra in Four Dimensions. Adv. Theor. Math. Phys. 4 (2002) ) J. Gray, Y. H. He, V. Jejjala, B. Jurke, B. D. Nelson, J. Simón. Calabi-Yau Manifolds with Large-Volume Vacua. Phys. Rev. D86 (2012) The Volume Calculation The simplest example of a Calabi-Yau manifold is one with only two two-cycles. The volume of such a manifold is given as V = t t 1 2 * t 2 + t 1 *t t 2 3 t 1 ∫ t t 1 2 * t 2 + t 1 * t t 2 3 Results Devised several important algorithms: Construction of any Calabi-Yau manifold Extension of Swiss Cheese search capabilities Identification of del Pezzo content State of the art allows identification of Swiss Cheese manifolds with fewer than 4 Kahler moduli. Results from those searches: Acknowledgments We thank E. Ebrahim for collaborations, and the Hamel Center for Undergraduate Research, the McNair Program, and NSF grant PHY for financial support. Systematic Analysis of Semi-Realistic String Compactifications Herbie Smith, Prof. Per Berglund Department of Physics, University of New Hampshire, Durham, NH Our Research Research Problem Identify Calabi-Yau manifolds that previous research suggests could resemble our cosmology and particle physics [2]. Extend the scope of previous work to find such models [3]. Analyze physical implications of these models. Method Devise algorithms to analyze Calabi-Yau manifolds constructed from four-dimensional reflexive polyhedra [4]. Focus on promising cosmological models originally studied in [2], called Swiss Cheese Calabi-Yau manifolds. Seek models with del Pezzo content, which gives rise to particle physics. # Kahler moduli # Calabi-Yau manifolds # Swiss Cheese manifolds # Swiss Cheese with del Pezzo content ,