Surface Operators from M-strings

It has been found that surface operators have a significant role in AGT relation. This duality is an outstanding consequence of M-theory, but it is actually encoded into the brane web for which the topological string can work. From this viewpoint, the surface defect in AGT relation is geometrically engineered as a toric brane realization. Also, there is a class of the brane configuration in M-theory called M-strings which can be translated into the language of the topological string. In this work, we propose a new M-string configuration which can realize AGT relation in the presence of the surface defect by utilizing the geometric transition in the refined topological string.

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