String theory and mathematical physics

Supplementary Material to Papers

Calabi-Yau Data Bases

One Parameter Hypergeometric Calabi-Yau higher genus data

  • The reference explaining the direct integration methods to obtain the higher Gopakumar Vafa (GV) invariants below is "Topological string theory on compact Calabi-Yau: Modularity and boundary conditions" by Minxin Huang, Albrecht Klemm and Seth Quakenbush arxiv:0612125
  • Arithmetic properties of the period on the hypergeometric models that follow from their Hasse Weil Zeta function have been studied in ``D-brane masses at special fibres of hypergeometric families of Calabi-Yau threefolds, modular forms, and periods", by Kilian Bönisch (see Master Thesis below), Albrecht Klemm, Emanuel Scheidegger and Don Zagier arxiv:2203.09246
  • In the work "Topological Strings on Non-Commutative Resolutions" by Sheldon Katz, Albrecht Klemm, Thorsten Schimannek and Eric Sharpe the second MUM point in the X2222(11111111) family has been identified with a non-commutative resolution of the X8(11114) model with Z2 torsion arxiv:2212.08655 . The list of Z2 torsion GV invariants can be found below. Note that the GV invariants for the X2222(11111111) model could only be calculated to genus 32 by combining conditions on the GV invariants at it's two MUM points.
  • New boundary conditions for the direct integration for most of the models were obtained in "Quantum Geometry, Stability and Modularity" by Sergei Alexandrov, Soheyla Feyzbakhsh, Albrecht Klemm, Boris Pioline and Thorsten Schimannek arxiv:2301.08066 , using wall-crossing to relate GV invariants to Donaldson-Thomas invariants with one unit of D4 brane charge (also known as D4-D2-D0 indices), and exploiting the conjectural modular properties of generating series of D4-D2-D0 indices to obtain GV invariants near the Castelnuovo bound. Extending this analysis, the boundary conditions have been improved in "Quantum geometry and mock modularity" arxiv:2312.12629 by Sergei Alexandrov, Soheyla Feyzbakhsh, Albrecht Klemm and Boris Pioline using wall-crossing formulas that relate now GV invariants to DT invariants with two units of D4 brane charge. The generating functions of the latter involve mock modular functions, which were fixed for X8(11114) and X10(11125). This determines the ambiguties theoretically up to genus 95 and 112. The data given below do not reach the theoretical bound, but check the relations.
  • The formal expansion of the Fg in terms of the propagators Szz,Sz,S and z are very huge data sets of crucial importance for the study of ``Non perturbative topological String Theory on Compact CY 3-folds", by Jie Gu, Amir Kashani-Poor, Albrecht Klemm and Marcos Marino arxiv:2305.19916