D-branes at Singularities and String Phenomenology

Abstract

In these notes we give an introduction to some of the concepts involved in constructing SM-like gauge theories in systems of branes at singularities of CY manifolds. These notes are an expanded version of lectures given by Herman Verlinde at the Cargese 2006 Summer School.

Figures (5)

• Figure 1: D(p+3)-branes may wrap $p$-cycles within the base $X$ of the Calabi-Yau singularity.
• Figure 2: Quiver theory of the cone over ${\mathbb{P}}^1\times{\mathbb{P}}^1$.
• Figure 3: The MSSM-like quiver gauge theory obtained in Verlinde:2005jr. Each line represents three generations of bi-fundamentals.
• Figure 4: Our proposed D3-brane realization of the MSSM involves a $dP_8$ singularity embedded inside a CY manifold, such that two of its 2-cycles, $\alpha_1$ and $\alpha_2$, develop an $A_2$ singularity, and all 2-cycles except $\alpha_4$ are non-trivial within the full CY.
• Figure 5: An MSSM-like quiver gauge theory, satisfying all rules for world-volume theories in an unoriented string models. A construction of this MSSM quiver theory via D-branes on a CY singularity has recently been given in Wijnholt:2007vn