Four ways across the wall

Details Four ways across the wall Four ways across the wall

2011-03-01

arxiv.org/abs/1103.0261v2

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, 2 figures, proceedings of the workshop "Algebra, Geometry and Mathematical Physics", Tj\"arn\"o, Sweden, 25-30 Octob

Scientific paper

An important question in the study of N=2 supersymmetric string or field theories is to compute the jump of the BPS spectrum across walls of marginal stability in the space of parameters or vacua. I survey four apparently different answers for this problem, two of which are based on the mathematics of generalized Donaldson-Thomas invariants (the Kontsevich-Soibelman and the Joyce-Song formulae), while the other two are based on the physics of multi-centered black hole solutions (the Coulomb branch and the Higgs branch formulae, discovered in joint work with Jan Manschot and Ashoke Sen). Explicit computations indicate that these formulae are equivalent, though a combinatorial proof is currently lacking.

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