A new framework maps microscopic inputs to universal properties of generic symmetry-enriched TQSLs and establishes a bijective crystalline equivalence principle between lattice-plus-internal and internal-only symmetry data.
Turaev-Viro invariants as an extended TQFT III
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abstract
In the third paper in this series, we examine the Reshetikhin-Turaev and Turaev-Viro TQFTs at the level of surfaces. In particular, we show that for a closed surface $\Sigma$, $Z_{TV, \mathcal{C}}(\Sigma) \cong Z_{RT, Z(\C)}(\Sigma)$, thus extending the equality of 3-manifold invariants proved in an earlier paper to an equivalence of TQFTs. We also describe how to compute Turaev-Viro state sums for 3-manifolds with embedded ribbon graphs.
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2026 1verdicts
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Microscopic universal theory of symmetry-enriched topological quantum spin liquids
A new framework maps microscopic inputs to universal properties of generic symmetry-enriched TQSLs and establishes a bijective crystalline equivalence principle between lattice-plus-internal and internal-only symmetry data.