The Seiberg-Witten Differential From M-Theory

TL;DR

The paper derives the Seiberg-Witten differential from an M-theory brane construction of 4D $N=2$ gauge theories by enforcing BPS conditions for a twobrane ending on a fivebrane. It shows that the twobrane area equals the pullback of the holomorphic 2-form $\\omega = ds \wedge dv$ and, via Stokes' theorem, yields the Seiberg-Witten differential $\\lambda_{SW} = v(t) \frac{dt}{t}$ on the curve $\\Sigma$, independent of the explicit curve. The construction applies to all classical gauge groups (with orientifolds and matter included) and provides a geometric interpretation of the beta function and the BPS spectrum in terms of holomorphic data. This offers a simple, physically transparent derivation that unifies M-theory brane pictures with the Seiberg-Witten integrable system framework.

Abstract

The form of the Seiberg-Witten differential is derived from the M-theory approach to N=2 supersymmetric Yang-Mills theories by directly imposing the BPS condition for twobranes ending on fivebranes. The BPS condition also implies that the pullback of the Kahler form onto the space part of the twobrane world-volume vanishes.