On refined Chern-Simons and refined ABJ matrix models
arXiv:2107.07525 · doi:10.1007/s11005-022-01518-1
Abstract
We consider the matrix model of refined Chern-Simons theory on for the unknot. We derive a -difference operator whose insertion in the matrix integral reproduces an infinite set of Ward identities which we interpret as -Virasoro constraints. The constraints are rewritten as difference equations for the generating function of Wilson loop expectation values which we solve as a recursion for the correlators of the model. The solution is repackaged in the form of superintegrability formulas for Macdonald polynomials. Additionally, we derive an equivalent -difference operator for a similar refinement of ABJ theory and show that the corresponding -Virasoro constraints are equal to those of refined Chern-Simons for a gauge super-group . Our equations and solutions are manifestly symmetric under Langlands duality which correctly reproduces 3d Seiberg duality when is a specific root of unity.
arXiv commentv2: 30 pages, minor revisions, added comments on relations to quantum mirror curves in Section 2.5, added comments on ABJ integrals in Appendix C, Lett.Math.Phys. version
References in corpus (41)
- N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
- Fractional M2-branes
- Chern-Simons theory, matrix integrals, and perturbative three-manifold invariants
- Matrix Model as a Mirror of Chern-Simons Theory
- A supermatrix model for N=6 super Chern-Simons-matter theory
- A Quantum Deformation of the Virasoro Algebra and the Macdonald Symmetric Functions
- Matrix factorizations and link homology II
- Torus knots and mirror symmetry
- Knot Homology from Refined Chern-Simons Theory
- Deformed quantum Calogero-Moser problems and Lie superalgebras
- Branes And Supergroups
- Macdonald's Evaluation Conjectures and Difference Fourier Transform
- Deformations of W-algebras associated to simple Lie algebras
- A-polynomial, B-model, and Quantization
- Ghost D-branes
- On the complete perturbative solution of one-matrix models
- Cohomological localization of Chern-Simons theory
- Correlators in tensor models from character calculus
- On (q,t)-deformation of Gaussian matrix model
- Sum rules for characters from character-preservation property of matrix models
- On matrix models and their -deformations
- 2d-4d Connection between q-Virasoro/W Block at Root of Unity Limit and Instanton Partition Function on ALE Space
- Wilson loops in supersymmetric Chern-Simons-matter theories and duality
- An elliptic Virasoro symmetry in 6d
- The Superpolynomial for Knot Homologies
- The deformed Virasoro algebra at roots of unity
- -Virasoro/W Algebra at Root of Unity and Parafermions
- Langlands duality for finite-dimensional representations of quantum affine algebras
- Solving q-Virasoro constraints
- Intersecting Defects and Supergroup Gauge Theory
- 3d Expansions of 5d Instanton Partition Functions
- Topological recursion and mirror curves
- Analytic Torsion, 3d Mirror Symmetry And Supergroup Chern-Simons Theories
- Quantization of Harer-Zagier formulas
- Hurwitz numbers and BKP hierarchy
- Super-Macdonald polynomials: Orthogonality and Hilbert space interpretation
- Exact SUSY Wilson loops on from -Virasoro constraints
- Towards U(N|M) knot invariant from ABJM theory
- Harer-Zagier formulas for knot matrix models
- On the Virasoro constraints for torus knots
- Elliptic Ruijsenaars difference operators, symmetric polynomials, and Wess-Zumino-Witten fusion rings