Trace identities for the topological vertex

• Jim Bryan ^[1] ; Martijn Kool ^[2] ; Benjamin Young ^[3]
  1. [1] University of British Columbia

     University of British Columbia

     Canadá

     
  2. [2] Utrecht University

     Utrecht University

     Países Bajos

     
  3. [3] University of Oregon

  Mostrar afiliaciones +
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 24, Nº. 2, 2018, págs. 1527-1548
• Idioma: inglés
• Enlaces
  • Texto completo (pdf)
• Resumen

  • The topological vertex is a universal series which can be regarded as an object in combinatorics, representation theory, geometry, or physics. It encodes the combinatorics of 3D partitions, the action of vertex operators on Fock space, the Donaldson–Thomas theory of toric Calabi–Yau threefolds, or the open string partition function of C3 . We prove several identities in which a sum over terms involving the topological vertex is expressed as a closed formula, often a product of simple terms, closely related to Fourier expansions of Jacobi forms. We use purely combinatorial and representation theoretic methods to prove our formulas, but we discuss applications to the Donaldson–Thomas invariants of elliptically fibered Calabi–Yau threefolds at the end of the paper.