Kirby Moves for 3d Gauge Theories

Abstract

The geometric engineering of 3d $\mathcal{N}=2$ gauge theories can be given by M5-branes on three-manifolds. We focus on the Dehn surgeries and Kirby moves of three-manifolds. We notice the Kirby move can be slightly extended when the chiral multiplets exist, and these chiral multiplets arise from Lagrangian M5-branes of the Ooguri-Vafa type in the cotangent bundles of three-manifolds. Through string dualities, we check that this M2-M5-brane configuration is consistent with 3d brane webs. We start from analyzing lens spaces as a toy model, and extend results to plumbed three-manifolds. We also show a basic 3d duality can be interpreted as Rolfsen twist.

arXiv comment29 pages, many figures