Surface Operators from M-strings

TL;DR

This paper proposes a new M-string configuration that geometrically engineers surface defects in the AGT relation using refined topological string theory and geometric transition techniques.

Contribution

It introduces a novel M-string setup that encodes surface operators within the AGT correspondence via topological string methods.

Findings

New M-string configuration for surface defects

Realization of AGT relation with surface defects

Application of geometric transition in refined topological string

Abstract

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.