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4 results for “half-index”

3d-3d correspondence and abelian flat connectionhep-th

The study connects knot complements to 3d theories via half-index calculations.

problem Understanding the relationship between knot complements and 3d theories.

method Using half-index calculations and inverted Habiro series, the study realizes knot complements as homological blocks.

result The colored Jones polynomial is derived from choosing specific poles in the half-index integral expression.

3d-3d correspondence homological blocks knot complements half-index inverted Habiro series

2026-03-05abs ↗pdf ↗

3d-3d correspondence for knot complements with finite and large

N

hep-th

Researchers map knot complements using 3d theories and half-index calculations.

problem Mapping knot complements using mathematical theories.

method Using 3d

\mathcal{N}=2

theories and half-index calculations.

result Realized homological blocks and HOMFLY-PT polynomials for knot complements.

knot complements 3d theories half-index HOMFLY-PT polynomial SU(N)

2026-07-23abs ↗pdf ↗

BPS spectra and 3-manifold invariantshep-th

We provide a physical definition of new homological invariants $\mathcal{H}_a (M_3)$ of 3-manifolds (possibly, with knots) labeled by abelian flat connections. The physical system in question involves a 6d fivebrane theory on $M_3$ times a 2-disk, $D^2$ , whose Hilbert space of BPS states plays the role of a basic build…

2017-01-23abs ↗pdf ↗

3d Modularity Revisitedhep-th

Researchers clarify modular group representations and vertex operator algebras for 3d invariants.

problem Understanding the full set of 3d invariants and their modular properties.

method Introducing supersymmetric defects and constructing cone vertex operator algebras.

result The full vector-valued quantum modular form for $\widetilde{ m SL}_2(\mathbb{Z})$ captures all $\hat Z$-invariants of a given three-manifold.

3d invariants modular forms vertex operator algebras supersymmetry mock modularity

2024-03-22abs ↗pdf ↗