2017/06/02 by A. Mironov, А. Миронов, A. Morozov +4 · 11 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics #Conifold #Gaussian #Gaussian integer #Genus #Geometric and Algebraic Topology #Knot (papermaking) #Knot theory #Logarithm #Mathematical analysis #Mathematical physics #Mathematics #Parameterized complexity #Physics #Pure mathematics #hep-th
paper · pdf · doi:10.1016/j.nuclphysb.2017.08.016
published in Nuclear Physics B 924, 1-32 (Elsevier BV) · 23 pages
arxiv created 2017/06/02 · openalex publication_date 2017/09/08 · arxiv updated 2017/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Recent advances in knot polynomial calculus allowed us to obtain a huge variety of LMOV integers counting degeneracy of the BPS spectrum of topological theories on the resolved conifold and appearing in the genus expansion of the plethystic logarithm of the Ooguri–Vafa partition functions. Already the very first look at this data reveals that the LMOV numbers are randomly distributed in genus (!) and are very well parameterized by just three parameters depending on the representation, an integer and the knot. We present an accurate formulation and evidence in support of this new puzzling observation about the old puzzling quantities. It probably implies that the BPS states, counted by the LMOV numbers can actually be composites made from some still more elementary objects.