Index for a model of 3d-3d correspondence for plumbed 3-manifolds

摘要

We consider theS2×qS1supersymmetric index of a 3dN=2theoryT[M3]whenM3is a plumbed 3-manifold. We engineer an effective description ofT[M3]from the expression of the homological block for plumbed 3-manifolds as aD2×qS1partition function of a 3dN=2theoryT[M3]with a boundary condition. We check that the supersymmetric index for such aT[M3]is invariant under the 3d Kirby moves.