10,583 research outputs found

    Covariance of WDVV equations

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    The (generalized) WDVV equations for the prepotentials in 2d2d topological and 4,5d4,5d Seiberg-Witten models are covariant with respect to non-linear transformations, described in terms of solutions of associated linear problem. Both time-variables and the prepotential change non-trivially, but period matrix (prepotential's second derivatives) remains intact.Comment: LaTeX, 7 pages, no figures (misprints corrected

    Towards effective topological field theory for knots

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    Construction of (colored) knot polynomials for double-fat graphs is further generalized to the case when "fingers" and "propagators" are substituting R-matrices in arbitrary closed braids with m-strands. Original version of arXiv:1504.00371 corresponds to the case m=2, and our generalizations sheds additional light on the structure of those mysterious formulas. Explicit expressions are now combined from Racah matrices of the type R⊗R⊗Rˉ⟶RˉR\otimes R\otimes\bar R\longrightarrow \bar R and mixing matrices in the sectors R⊗3⟶QR^{\otimes 3}\longrightarrow Q. Further extension is provided by composition rules, allowing to glue two blocks, connected by an m-strand braid (they generalize the product formula for ordinary composite knots with m=1).Comment: 10 pages + table in Appendi
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