2019/10/31 by Tobias Ekholm, Piotr Kucharski, Pietro Longhi
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Class (philosophy) #Embedding #Geometric and Algebraic Topology #Holomorphic function #Quiver #Relation (database) #Representation theory #Skein #Skein relation #Torus #hep-th #math.GT #math.SG
paper · pdf · doi:10.1007/jhep02(2020)018
published as JHEP 02 (2020) 018 · 43+5 pages
openalex created_date 2019/10/18 · openalex publication_date 2020/02/01 · arxiv created 2020/02/11 · arxiv updated 2020/02/12 · openalex updated_date 2026/08/06
A bstract The relation between open topological strings and representation theory of symmetric quivers is explored beyond the original setting of the knot-quiver correspondence. Multiple cover generalizations of the skein relation for boundaries of holomorphic disks on a Lagrangian brane are observed to generate dual quiver descriptions of the geometry. Embedding into M-theory, a large class of dualities of 3d N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2 theories associated to quivers is obtained. The multi-cover skein relation admits a compact formulation in terms of quantum torus algebras associated to the quiver and in this language the relations are similar to wall-crossing identities of Kontsevich and Soibelman.