曲面算子、Bubbling Calabi-Yau和AGT关系
Surface Operator, Bubbling Calabi-Yau and AGT Relation
摘要：
N=2四维规范理论中的曲面算符是有趣的半BPS对象。这些算子继承了规范理论与刘维共形场论的联系，刘维场论是由Alday，Gaiotto和Tachikawa发现的。此外，有人提出，环面膜的A-模型拓扑弦导致表面运营商通过几何工程。我们利用拓扑弦论对曲面算子进行了分析。从这个观点出发，我们提出拓扑开弦振幅的波函数行为几何地设计了相应规范理论的表面算符配分函数和Gaiotto曲线.然后，我们研究了一个奇特的功能，表面操作符对应于插入的退化领域的共形场论的一面。我们表明，这方面可以实现为拓扑弦论中的几何过渡，并插入一个表面操作导致的复曲面Calabi-Yau几何冒泡。
英文摘要：
Surface operators in N=2 four-dimensional gauge theories are interesting half-BPS objects. These operators inherit the connection of gauge theory with the Liouville conformal field theory, which was discovered by Alday, Gaiotto and Tachikawa. Moreover it has been proposed that toric branes in the A-model topological strings lead to surface operators via the geometric engineering. We analyze the surface operators by making good use of topological string theory. Starting from this point of view, we propose that the wave-function behavior of the topological open string amplitudes geometrically engineers the surface operator partition functions and the Gaiotto curves of corresponding gauge theories. We then study a peculiar feature that the surface operator corresponds to the insertion of the degenerate fields in the conformal field theory side. We show that this aspect can be realized as the geometric transition in topological string theory, and the insertion of a surface operator leads to the bubbling of the toric Calabi-Yau geometry.
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