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Index for a Model of 3d-3d Correspondence for Plumbed 3-Manifolds
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abstract
We consider the $S^2 \times_q S^1$ supersymmetric index of a 3d $\mathcal{N}=2$ theory $T[M_3]$ when $M_3$ is a plumbed 3-manifold. We engineer an effective description of $T[M_3]$ from the expression of the homological block for plumbed 3-manifolds as a $D^2 \times_q S^1$ partition function of a 3d $\mathcal{N}=2$ theory $T[M_3]$ with a boundary condition. We check that the supersymmetric index for such a $T[M_3]$ is invariant under the 3d Kirby moves.
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Cited by 1 Pith paper
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3d $\mathcal{N}=$ 4 rank-0 SCFT from punctured lens space
The Gang-Kim-Stubbs rank-0 SCFT is derived from the Dimofte-Gaiotto-Gukov construction on a punctured lens space, and a new family of theories plus a self-mirror conjecture are proposed from other lens spaces.
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