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Quantum Riemann Surfaces in Chern-Simons Theory

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arxiv 1102.4847 v3 pith:3GYBUOKD submitted 2011-02-23 hep-th math.GTmath.QA

Tudor Dimofte This is my paper
classification hep-thmath.GTmath.QA
keywords chern-simonsa-hatcomplementgluingknotoperatorpartitiontheory
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We construct from first principles the operator 'A-hat' that annihilates the partition functions (or wavefunctions) of three-dimensional Chern-Simons theory with gauge groups SU(2), SL(2,R), or SL(2,C) on a knot complement M. The operator 'A-hat' is a quantization of the knot complement's classical A-polynomial A(l,m). The construction proceeds by decomposing three-manifolds into ideal tetrahedra, and invoking a new, more global understanding of gluing in TQFT to put them back together. We advocate in particular that, properly interpreted, "gluing = symplectic reduction." We also arrive at a new finite-dimensional state integral model for computing the analytically continued "holomorphic blocks" that compose any physical Chern-Simons partition function.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Three-dimensional TQFTs from Argyres--Douglas theories via the 3d/3d correspondence

    hep-th 2026-07 conditional novelty 7.0 of 10

    The twisted circle reduction of the (A1,A2n) Argyres-Douglas theory is realized as a DGG abelian Chern-Simons-matter theory on the lens space L(2n+3,2k), with maximal (one-less-than-maximal) monopole superpotential fl...

  2. Parabolic skein modules

    math.QA 2025-05 conditional novelty 7.0 of 10

    Parabolic defect skein theory yields a new, triangulation-based definition and computation of the quantum A-ideal of knots, matching known classical limits.

  3. Solving the tetrahedron equation by Teichm\"uller TQFT

    math-ph 2026-02 conditional novelty 6.0 of 10

    Boltzmann weights built from Teichmüller TQFT on shaped triangulations with line defects exactly solve the bicolored tetrahedron equations.

  4. Statistics in 3d gravity from knots and links

    hep-th 2025-08 conditional novelty 6.0 of 10

    Fragmentation of knots and links by Wilson lines builds wormhole amplitudes that give non-perturbative Gaussian and non-Gaussian corrections to OPE statistics in 3d gravity and CFT2.

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