String theory and the Kauffman polynomial

Details String theory and the Kauffman polynomial String theory and the Kauffman polynomial

2009-04-07

arxiv.org/abs/0904.1088v3

Physics

High Energy Physics

High Energy Physics - Theory

36 pages, many figures; references and examples added, typos corrected, final version to appear in CMP

Scientific paper

We propose a new, precise integrality conjecture for the colored Kauffman polynomial of knots and links inspired by large N dualities and the structure of topological string theory on orientifolds. According to this conjecture, the natural knot invariant in an unoriented theory involves both the colored Kauffman polynomial and the colored HOMFLY polynomial for composite representations, i.e. it involves the full HOMFLY skein of the annulus. The conjecture sheds new light on the relationship between the Kauffman and the HOMFLY polynomials, and it implies for example Rudolph's theorem. We provide various non-trivial tests of the conjecture and we sketch the string theory arguments that lead to it.

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