摘要: We formulate a refinement of SU(N) Chern-Simons theory on three-manifold via the refined topological string and (2,0) N M5 branes. The is defined any with semi-free circle action. give an explicit solution theory, in terms one-parameter S T matrices related to Macdonald polynomials. ordinary are similar many ways; for example, Verlinde formula holds both. obtain new invariants Seifert three-manifolds torus knots inside them. conjecture that knot we compute Poincare polynomials sl(n) homology theory. latter includes Khovanov-Rozansky homology, as special case. passes number nontrivial checks. show that, large colored fundamental representation SU(N), our agree homology. As byproduct, S^3 has large-N dual which X=O(-1)+O(-1)->P^1; this supports by Gukov, Schwarz Vafa relating spectrum BPS states X also provide matrix model description some amplitudes S^3.
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