CoulombHiggs

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, http://www.lpthe.jussieu.fr/ pioline/computing.html