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

Abstract

We consider the S2×qS1 supersymmetric index of a 3d N=2 theory T[M3] when M3 is a plumbed 3-manifold. We engineer an effective description of T[M3] from the expression of the homological block for plumbed 3-manifolds as a D2×qS1 partition function of a 3d N=2 theory T[M3] with a boundary condition. We check that the supersymmetric index for such a T[M3] is invariant under the 3d Kirby moves.