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Rozansky-Witten geometry of Coulomb branches and logarithmic knot invariants

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arxiv 2005.05347 v1 pith:I2TGBCVX submitted 2020-05-11 hep-th math.AGmath.GTmath.QAmath.RT

Sergei Gukov , Po-Shen Hsin , Hiraku Nakajima , Sunghyuk Park , Du Pei , Nikita Sopenko This is my paper
classification hep-thmath.AGmath.GTmath.QAmath.RT
keywords invariantsknotrozansky-wittenaffineakutsu-deguchi-ohtsukiavenuesbranchesconnections
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abstract

By studying Rozansky-Witten theory with non-compact target spaces we find new connections with knot invariants whose physical interpretation was not known. This opens up several new avenues, which include a new formulation of $q$-series invariants of 3-manifolds in terms of affine Grassmannians and a generalization of Akutsu-Deguchi-Ohtsuki knot invariants.

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Cited by 2 Pith papers

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

  1. A supergroup series for knot complements

    math.GT 2025-08 unverdicted novelty 7.0 of 10

    Defines the three-variable superalgebra series F_K(y,z,q) for knot complements, derives its surgery relation to hat Z(q), and computes examples for torus knots.

  2. Quantum invariants of 3-manifolds and links: a review

    math-ph 2025-09 unverdicted novelty 1.0 of 10

    This is a survey, not a new result: it reviews the q-series invariants Zhat, F_K, F_L and their supergroup analogues, collecting known conjectures, theorems, and examples.

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