**Title:** Bubbling Calabi-Yau geometry

**Speaker:** Takuya Okuda

**Speaker Info:** UCSB

**Brief Description:**

**Special Note**:

**Abstract:**

A saddle point of an integral beck-reacts when the integrand is multiplied by a large function. In gauge/gravity duality, the space-time (in gravity) representing a saddle point gets deformed when an operator is inserted in gauge theory path integral. The new space-time develops many new cycles carrying flux quantum numbers, and is called the bubbling geometry.First, basic examples from AdS/CFT will be intuitively explained, where the anti-de Sitter space back-reacts. Second, the idea of bubbling will be applied to the gauge/gravity (large N) duality of the topological string. In Chern-Simons gauge theory, I will consider the Wilson loop along a knot in three-sphere. I will argue that the conifold back-reacts to the Wilson loop and produces a new bubbling geometry. So bubbling conjecturally associates a six-manifold to a knot. I will present explicit bubbling Calabi-Yau geometries that are dual to the unknot in three-sphere and lens spaces. Third, if there is time, I will show that the BPS invariants of any Lagrangian brane determine the BPS invariants of the six-fold related by geometric transition.

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