Vortex Counting and Lagrangian 3-manifolds - High Energy Physics - TheoryReport as inadecuate

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Abstract: To every 3-manifold M one can associate a two-dimensional N=2,2supersymmetric field theory by compactifying five-dimensional N=2super-Yang-Mills theory on M. This system naturally appears in the study ofhalf-BPS surface operators in four-dimensional N=2 gauge theories on one hand,and in the geometric approach to knot homologies, on the other. We study therelation between vortex counting in such two-dimensional N=2,2 supersymmetricfield theories and the refined BPS invariants of the dual geometries. Incertain cases, this counting can be also mapped to the computation ofdegenerate conformal blocks in two-dimensional CFT-s. Degenerate limits ofvertex operators in CFT receive a simple interpretation via geometrictransitions in BPS counting.

Author: Tudor Dimofte, Sergei Gukov, Lotte Hollands

Source: https://arxiv.org/

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