Instanton Counting and Donaldson-Thomas Theory on Toric Calabi-Yau Four-Orbifolds

Richard J. Szabo, Michelangelo Tirelli

Research output: Working paperPreprint

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Abstract

We study rank r cohomological Donaldson-Thomas theory on a toric Calabi-Yau orbifold of C4 by a finite abelian subgroup Γ of SU(4), from the perspective of instanton counting in cohomological gauge theory on a noncommutative crepant resolution of the quotient singularity. We describe the moduli space of noncommutative instantons on C4/Γ and its generalized ADHM parametrization. Using toric localization, we compute the orbifold instanton partition function as a combinatorial series over r-vectors of Γ-coloured solid partitions. When the Γ-action fixes an affine line in C4, we exhibit the dimensional reduction to rank r Donaldson-Thomas theory on the toric Kahler three-orbifold C3/Γ. Based on this reduction and explicit calculations, we conjecture closed infinite product formulas, in terms of generalized MacMahon functions, for the instanton partition functions on the orbifolds C2/Zn×C2 and C3/(Z2×Z2)×C, finding perfect agreement with new mathematical results of Cao, Kool and Monavari.
Original languageEnglish
PublisherarXiv
Publication statusPublished - 30 Jan 2023

Keywords

  • hep-th
  • math-ph
  • math.AG
  • math.MP
  • math.QA

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