String-Math 2012
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Publication:3453906
DOI10.1090/PSPUM/090zbMATH Open1329.00194arXiv1303.3709OpenAlexW3122079618MaRDI QIDQ3453906
Author name not available (Why is that?)
Publication date: 1 December 2015
Published in: (Search for Journal in Brave)
Abstract: We review a construction of a new class of algebraic curves, called super-A-polynomials, and their quantum generalizations. The super-A-polynomial is a two-parameter deformation of the A-polynomial known from knot theory or Chern-Simons theory with SL(2,C) gauge group. The two parameters of the super-A-polynomial encode, respectively, the t-deformation which leads to the "refined A-polynomial", and the Q-deformation which leads to the augmentation polynomial of knot contact homology. For a given knot, the super-A-polynomial encodes the asymptotics of the corresponding S^r-colored HOMFLY homology for large r, while the quantum super-A-polynomial provides recursion relations for such homology theories for each r. The super-A-polynomial also admits a simple physical interpretation as the defining equation for the space of SUSY vacua in a circle compactification of the effective 3d N=2 theory associated to a given knot (complement). We discuss properties of super-A-polynomials and illustrate them in many examples.
Full work available at URL: https://arxiv.org/abs/1303.3709
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