Review of "Quantum field theory and the Jones polynomial."

By P. Mullhaupt. 2008

379 citations recorded by the source corpus.

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Averaging over Narain moduli space (2020, unknown): “Instead of boundary gravitons, the Chern-Simon theory, if treated as in [28], has chiral and anti-chiral boundary current algebras which are abelian (since in this case we are studying an abelian gauge theory) and are each of rank D (because of the signature of the quadratic form).”
Fractional quantum Hall effect via holography: Chern-Simons, edge states and hierarchy (2009, methodology): “Indeed we can show that it becomes the log of the partition function Z(S3) of Chern-Simons theory on S3 [33] using the standard surgery method [5].”
Free partition functions and an averaged holographic duality (2020, unknown): “In [86] Witten established an exact equivalence between Chern-Simons gauge theory and rational CFT.”
Quantum Riemann Surfaces in Chern-Simons Theory (2011, methodology): “Physically, the colored Jones polynomial JN(K, q) is the non-analytically-continued SU(2) Chern-Simons partition function on the three-manifold M = S(3), with the insertion of a Wilson loop operator along a knot K [8, 9, 10].”
Generalized volume conjecture and the A-polynomials: The Neumann–Zagier potential function as a classical limit of the partition function (2006, methodology): “Since the quantum invariant of knots/links and 3-manifolds as a generalization of the Jones polynomial [25] is constructed by Witten [53] by use of the Chern–Simons path integral, studies on quantum invariants have been much developed.”