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Supervariable approach to particle on a torus knot: a model for Hodge theory
We analyze a particle constrained to move on a ( p , q )-torus knot within the framework of supervariable approach and deduce the BRST as well as...
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Knot Invariants and Configuration Space Integrals
After a short presentation of the theory of Vassiliev knot invariants, we shall introduce a universal finite type invariant for knots in the ambient...
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Knot homologies and generalized quiver partition functions
We introduce generalized quiver partition functions of a knot K and conjecture a relation to generating functions of symmetrically colored HOMFLY-PT...
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Machine learning of knot topology in non-Hermitian band braids
The deep connection among braids, knots and topological physics has provided valuable insights into studying topological states in various physical...
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BPS invariants for a Knot in Seifert manifolds
We calculate homological blocks for a knot in Seifert manifolds when the gauge group is SU( N ). We obtain the homological blocks with a given...
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Towards Catastrophe Theory for Khovanov–Rozansky Homology
We suggest another way to look at observables in cohomological quantum field theory, which are the Khovanov–Rozansky knot invariants. To do that, we...
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Topological entanglement entropy for torus-knot bipartitions and the Verlinde-like formulas
The topological Rényi and entanglement entropies depend on the bipartition of the manifold and the choice of the ground states. However, these...
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Resurgence in complex Chern-Simons theory at generic levels
In this note we study the resurgent structure of sl (2 , ℂ) Chern-Simons state integral model on knot complements S 3 \ 4 1 , S 3 \ 5 2 with generic discrete...
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The Resurgent Structure of Quantum Knot Invariants
The asymptotic expansion of quantum knot invariants in complex Chern–Simons theory gives rise to factorially divergent formal power series. We...
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Overview of Knot Invariants at Roots of Unity
We discuss different invariants of knots and links that depend on a primitive root of unity. We clarify the definitions of existing invariants with...
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The massive supermembrane on a knot
We obtain the Hamiltonian formulation of the 11D Supermembrane theory non-trivially compactified on a twice punctured torus times a 9D Minkowski...
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Fermions on a torus knot
In this work, we investigate the effects of a nontrivial topology (and geometry) of a system considering interacting and noninteracting particle...
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Twist Knot Invariants and Volume Conjecture
Chern–Simons theory provides a natural framework to construct a variety of knot invariants. The calculation of colored HOMFLY-PT polynomials of knots...
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Rigor with machine learning from field theory to the Poincaré conjecture
Despite their successes, machine learning techniques are often stochastic, error-prone and blackbox. How could they then be used in fields such as...
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Chern-Simons theory, Ehrhart polynomials, and representation theory
The Hilbert space of level q Chern-Simons theory of gauge group G of the ADE type quantized on T 2 can be represented by points that lie on the...
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Tidal surface states as fingerprints of non-Hermitian nodal knot metals
Non-Hermitian nodal knot metals (NKMs) contain intricate complex-valued energy bands which give rise to knotted exceptional loops and new topological...
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