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Framed knots at large $$N$$. (English) Zbl 1042.81071
Adem, Alejandro (ed.) et al., Orbifolds in mathematics and physics. Proceedings of a conference on mathematical aspects of orbifold string theory, Madison, WI, USA, May 4–8, 2001. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-2990-4/pbk). Contemp. Math. 310, 185-204 (2002).
Summary: We study the framing dependence of the Wilson loop observable of $$U(N)$$ Chern-Simons gauge theory at large $$N$$. Using proposed geometrical large $$N$$ dual, this leads to a direct computation of certain topological string amplitudes in a closed form. This yields new formulae for intersection numbers of cohomology classes on moduli of Riemann surfaces with punctures (including all the amplitudes of pure topological gravity in two dimensions). The reinterpretation of these computations in terms of BPS degeneracies of domain walls leads to novel integrality predictions for these amplitudes. Moreover we find evidence that large $$N$$ dualities are more naturally formulated in the context of $$U(N)$$ gauge theories rather than $$SU(N)$$.
For the entire collection see [Zbl 1003.00015].

##### MSC:
 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 58D30 Applications of manifolds of mappings to the sciences 81T10 Model quantum field theories 81R12 Groups and algebras in quantum theory and relations with integrable systems 81T13 Yang-Mills and other gauge theories in quantum field theory
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