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Outline
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Just like Periodic Table of chemical elements
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Periodic table of Knots
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Knot Equivalence
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Knot Invariant through recursive method
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Jones Polynomial
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Chern-Simons Theory
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Well-Known polynomials from Chern-Simons
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Knot Invariants from Chern-Simons
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Example: Trefoil invariant
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Eigenbasis of Braiding operator
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Polynomial invariant of trefoil
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Trefoil evaluation continued
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Figure 8 knot invariant
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Broad classification of knots
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Arborescent Knots
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10152 and 1071 arborescent knots
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Building blocks
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Equivalent Building Blocks
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Arborescent knot- Feynman diagram analogy
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Family Approach: Arborescent knots
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Arborescent knot invariants
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Do we know duality matrix elements
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Detection of Mutation
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[2,1] colored HOMFLY-PT
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Additional information in mixed representation
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Mutation operation on two-tangles
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Tangle and its My mutation
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Knot invariant for the mutant pair
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Knot Polynomials
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Reasons for Integer coefficients
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Khovanov Homology
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Chain Complex
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The vector space
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Homological Invariant
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Gauge-string duality in topological strings
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Duality in topological strings
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Topological String duality contd
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Open topological string amplitudes
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N integers from knot polynomials
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VERIFICATION USING KNOT INVARIANTS
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Can we write InZ [M] as closed string expansion?
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InZM contd
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Subtle Issues
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Generalization of the duality to SO gauge groups
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Oriented contribution
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Witten's Intersecting brane Construction
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Witten's intersecting brane constructioncontd
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M-Theory description of Witten's model
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Sourcing 0 term
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Model A: Witten model
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Two NS5-branes with relative orientation from Witten model
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Relation to Ooguri-Vafa model
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M-Theory description dual to Ooguri-Vafa
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Summary and Open problems
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Q&A
Description:
Explore knot polynomials and their connections to Chern-Simons field theory and string theory in this comprehensive lecture. Delve into topics such as knot invariants, Jones polynomials, and Chern-Simons theory. Examine arborescent knots, mutation detection, and Khovanov homology. Investigate gauge-string duality in topological strings and Witten's intersecting brane construction. Learn about the periodic table of knots, polynomial invariants for various knot types, and the relationship between knot theory and physics. Gain insights into advanced concepts like M-theory descriptions and open topological string amplitudes. Suitable for researchers and students in theoretical physics and mathematics interested in the intersection of knot theory, quantum field theory, and string theory.

Knot Polynomials from Chern-Simons Field Theory and Their String Theoretic Implications by P. Ramadevi

International Centre for Theoretical Sciences
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#Mathematics #Polynomials #Science #Physics #Theoretical Physics #String Theory #Representation Theory #Quantum Mechanics #Quantum Field Theory #Knot Theory #Khovanov Homology #Geometry #Topology #Knot Invariants
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Outline