BPS dyons and Hesse flow

Abstract

We revisit BPS solutions to classical N=2 low energy effective gauge theories. It is shown that the BPS equations can be solved in full generality by the introduction of a Hesse potential, a symplectic analog of the holomorphic prepotential. We explain how for non-spherically symmetric, non-mutually local solutions, the notion of attractor flow generalizes to gradient flow with respect to the Hesse potential. Furthermore we show that in general there is a non-trivial magnetic complement to this flow equation that is sourced by the momentum current in the solution.

25 pages, references added

References in corpus (7)

• Wall-Crossing from Boltzmann Black Hole Halos
• Magnetic Monopole Dynamics, Supersymmetry, and Duality
• Framed BPS States, Moduli Dynamics, and Wall-Crossing
• Seiberg-Witten Geometries Revisited
• Instantons, black holes and harmonic functions
• Real symplectic formulation of local special geometry
• Observations on the Darboux coordinates for rigid special geometry

Cited by in corpus (5)

• The Hesse potential, the c-map and black hole solutions
• Non-holomorphic deformations of special geometry and their applications
• BPS Spectrum, Indices and Wall Crossing in N=4 Supersymmetric Yang-Mills Theories
• On the sigma-model of deformed special geometry
• Attractor Flow Versus Hesse Flow in Wall-Crossing Structures