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We try to give a geometric construction of 3d $\mathcal{N}=2$ gauge theoriesusing three-manifolds and Dehn surgeries. It is known that wrapping M5-braneson plumbing three-manifolds leads to 3d theories with mixed Chern-Simonslevels. We find that this construction can be extended by adding Lagrangiandefects on the tangent bundles of three-manifolds. After wrapping M5-branes onthese defects and through M-theory/IIB string duality, one can get D5-branesthat introduce chiral multiplets. This is analogous to Ooguri-Vafa constructionof Wilson loop operators along knots on the three-sphere. In this note, we onlyconsider unknotted matter circles, which are intersections between defectM5-branes and plumbing manifolds. After introducing matters, mirror dualitiesof 3d theories match with Kirby moves of plumbing manifolds. We also find thedictionary between various structures of three-manifolds and physical aspectsof 3d gauge theories.

Surgery Constructions for 3d Theories, Part I: Matter Circles and Links