Branes and integrability in the N=2 SUSY YM theory

TL;DR

This paper proposes a brane-based interpretation of the integrable systems underlying the exact solutions of N=2 supersymmetric Yang-Mills theory, linking brane dynamics to spectral curves and monopole scattering.

Contribution

It introduces a novel brane perspective on the integrable models in N=2 SUSY YM theory, connecting collective brane coordinates to Calogero systems and spectral surfaces.

Findings

Spectral Riemann surfaces originate from brane collective coordinates.

Second integrable system models low energy brane scattering.

Brane interpretation provides insight into the integrable structure of the theory.

Abstract

We suggest the brane interpretation of the integrable dynamics behind the exact solution to the N=2 SUSY YM theory. Degrees of freedom of the Calogero type integrable system responsible for the appearance of the spectral Riemann surfaces originate from the collective coordinates of the dynamical branes. The second Whitham type integrable system corresponds to the low energy scattering of branes similar to the scattering of the magnetic monopoles.