MISC

査読有り
2013年2月

Super-A-polynomial for knots and BPS states

NUCLEAR PHYSICS B
  • Hiroyuki Fuji
  • ,
  • Sergei Gukov
  • ,
  • Piotr Sulkowski

867
2
開始ページ
506
終了ページ
546
記述言語
英語
掲載種別
DOI
10.1016/j.nuclphysb.2012.10.005
出版者・発行元
ELSEVIER SCIENCE BV

We introduce and compute a 2-parameter family deformation of the A-polynomial that encodes the color dependence of the superpolynomial and that, in suitable limits, reduces to various deformations of the A-polynomial studied in the literature. These special limits include the t-deformation which leads to the "refined A-polynomial" introduced in the previous work of the authors and the Q-deformation which leads, by the conjecture of Aganagic and Vafa, to the augmentation polynomial of knot contact homology. We also introduce and compute the quantum version of the super-A-polynomial, an operator that encodes recursion relations for S-r-colored HOMFLY homology. Much like its predecessor, the super-A-polynomial admits a simple physical interpretation as the defining equation for the space of SUSY vacua (= critical points of the twisted superpotential) in a circle compactification of the effective 3d N = 2 theory associated to a knot or, more generally, to a 3-manifold M. Equivalently, the algebraic curve defined by the zero locus of the super-A-polynomial can be thought of as the space of open string moduli in a brane system associated with M. As an inherent outcome of this work, we provide new interesting formulas for colored superpolynomials for the trefoil and the figure-eight knot. (C) 2012 Elsevier B.V. All rights reserved.

Web of Science ® 被引用回数 : 48

リンク情報
DOI
https://doi.org/10.1016/j.nuclphysb.2012.10.005
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000311972400015&DestApp=WOS_CPL

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