BPS dyons and Hesse flow

TL;DR

This paper introduces a Hesse potential to solve BPS equations in N=2 gauge theories, generalizing attractor flow to gradient flow and revealing a magnetic component influenced by momentum currents.

Contribution

It presents a novel symplectic approach using the Hesse potential to solve BPS equations and extends the concept of attractor flow to non-spherical, non-mutually local solutions.

Findings

Hesse potential provides a general solution method for BPS equations.

Attractor flow generalizes to gradient flow with respect to the Hesse potential.

A magnetic complement to the flow equation is identified, sourced by momentum currents.

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.