Rozansky-Witten geometry of Coulomb branches and logarithmic knot invariants

2020/05/11 by Sergei Gukov, Po-Shen Hsin, Hiraku Nakajima +3 · 51 citations
Mathematics · Physics and Astronomy · #Affine transformation #Algebraic Geometry and Number Theory #Cohomology #Geometric and Algebraic Topology #Gromov–Witten invariant #Homotopy and Cohomology in Algebraic Topology #Knot (papermaking) #Knot invariant #Knot theory #Mathematics #Pure mathematics #Quantum cohomology #hep-th #math.AG #math.GT #math.QA #math.RT

paper · pdf · doi:10.1016/j.geomphys.2021.104311

published in Journal of Geometry and Physics 168, 104311 (Elsevier BV) · 33 pages, 1 figure, 7 tables

arxiv created 2020/05/11 · openalex created_date 2020/05/21 · openalex publication_date 2021/06/17 · arxiv updated 2021/07/14 · openalex updated_date 2026/08/05

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.

Citations

• The Self-Duality Equations on a Riemann Surface
• The Universal Perturbative Quantum 3-manifold Invariant, Rozansky-Witten Invariants, and the Generalized Casson Invariant
• Modular Group Representations and Fusion in Logarithmic Conformal Field Theories and in the Quantum Group Center
• Métriques kählériennes et fibrés holomorphes
• The Verlinde formula for Higgs bundles
• Argyres-Douglas theories, chiral algebras and wild Hitchin characters
• The center of small quantum groups II: singular blocks
• 3d TQFTs from Argyres-Douglas theories
• Twisted indices of 3d N = 4 gauge theories and enumerative geometry of quasi-maps
• Equivariant Verlinde Formula from Fivebranes and Vortices
• The ADO Invariants are a q-Holonomic Family
• Rozansky-Witten theory, Localised then Tilted

Cited by

• BPS indices, modularity and perturbations in quantum K-theory