The Mathematica package CoulombHiggs.m allows to compute the Poincar-Laurent polynomial of the moduli space of stable representations of quivers using the Coulomb branch and Higgs branch formulae. The latter is based on Reineke’s solution to the Harder-Narasimhan recursion [1] and applies to quivers without oriented closed loops, while the former is based on a physical picture of BPS states as bound states of elementary ’single-centered’ constitutents, and applies to any quivers with or without oriented loops [2{4]. The first version of this package was released together with the preprint [5] where a general algorithm for computing the index of the quantum mechanics of multi-centered BPS black holes (the Coulomb index) was outlined. The second version 2.0, released along with the preprint [6], allowed to compute the Dolbeault-Laurent polynomial, relax assumptions on single-centered indices for basis vectors, study the effect of generalized mutations, and more. The third version 2.1, released along with the review [7], has been optimized to speed up the evaluation of Coulomb indices. The package file CoulombHiggs.m and various example files can be obtained from the second named author’s webpage, pioline/computing.html

References in zbMATH (referenced in 22 articles , 1 standard article )

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  1. Beaujard, Guillaume; Manschot, Jan; Pioline, Boris: Vafa-Witten invariants from exceptional collections (2021)
  2. Duan, Zhihao; Ghim, Dongwook; Yi, Piljin: 5D BPS quivers and KK towers (2021)
  3. Alexandrov, Sergei; Pioline, Boris: Black holes and higher depth mock modular forms (2020)
  4. Çanakçı, İlke; Lampe, Philipp: An expansion formula for type (A) and Kronecker quantum cluster algebras (2020)
  5. Beaujard, Guillaume; Mondal, Swapnamay; Pioline, Boris: Quiver indices and abelianization from Jeffrey-Kirwan residues (2019)
  6. Galakhov, Dmitry: BPS Hall algebra of scattering Hall states (2019)
  7. Panfil, Miłosz; Sułkowski, Piotr: Topological strings, strips and quivers (2019)
  8. Cirafici, Michele: Quivers, line defects and framed BPS invariants (2018)
  9. Del Zotto, Michele; Sen, Ashoke: About the absence of exotics and the Coulomb branch formula (2018)
  10. Manschot, Jan; Pioline, Boris; Sen, Ashoke: The Coulomb branch formula for quiver moduli spaces (2017)
  11. Gaddam, Nava: Elliptic genera from multi-centers (2016)
  12. Lee, Seung-Joo; Yi, Piljin: Witten index for noncompact dynamics (2016)
  13. Anninos, Dionysios; Anous, Tarek; de Lange, Paul; Konstantinidis, George: Conformal quivers and melting molecules (2015)
  14. Anninos, Dionysios; Anous, Tarek; Denef, Frederik; Peeters, Lucas: Holographic vitrification (2015)
  15. Hori, Kentaro; Kim, Heeyeon; Yi, Piljin: Witten index and wall crossing (2015)
  16. Kim, Heeyeon: Scaling behaviour of quiver quantum mechanics (2015)
  17. Kim, Heeyeon; Lee, Seung-Joo; Yi, Piljin: Mutation, Witten index, and quiver invariant (2015)
  18. Young, Matthew B.: Self-dual quiver moduli and orientifold Donaldson-Thomas invariants (2015)
  19. Chowdhury, Abhishek; Garavuso, Richard S.; Mondal, Swapnamay; Sen, Ashoke: BPS state counting in (N=8) supersymmetric string theory for pure D-brane configurations (2014)
  20. Córdova, Clay; Neitzke, Andrew: Line defects, tropicalization, and multi-centered quiver quantum mechanics (2014)

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