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

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.

Outline
Just like Periodic Table of chemical elements
Periodic table of Knots
Knot Equivalence
Knot Invariant through recursive method
Jones Polynomial
Chern-Simons Theory
Well-Known polynomials from Chern-Simons
Knot Invariants from Chern-Simons
Example: Trefoil invariant
Eigenbasis of Braiding operator
Polynomial invariant of trefoil
Trefoil evaluation continued
Figure 8 knot invariant
Broad classification of knots
Arborescent Knots
10152 and 1071 arborescent knots
Building blocks
Equivalent Building Blocks
Arborescent knot- Feynman diagram analogy
Family Approach: Arborescent knots
Arborescent knot invariants
Do we know duality matrix elements
Detection of Mutation
[2,1] colored HOMFLY-PT
Additional information in mixed representation
Mutation operation on two-tangles
Tangle and its My mutation
Knot invariant for the mutant pair
Knot Polynomials
Reasons for Integer coefficients
Khovanov Homology
Chain Complex
The vector space
Homological Invariant
Gauge-string duality in topological strings
Duality in topological strings
Topological String duality contd
Open topological string amplitudes
N integers from knot polynomials
VERIFICATION USING KNOT INVARIANTS
Can we write InZ [M] as closed string expansion?
InZM contd
Subtle Issues
Generalization of the duality to SO gauge groups
Oriented contribution
Witten's Intersecting brane Construction
Witten's intersecting brane constructioncontd
M-Theory description of Witten's model
Sourcing 0 term
Model A: Witten model
Two NS5-branes with relative orientation from Witten model
Relation to Ooguri-Vafa model
M-Theory description dual to Ooguri-Vafa
Summary and Open problems
Q&A