Branes and Calibrated Geometries

TL;DR

This paper explores how intersecting fivebranes in eleven-dimensional theory lead to BPS configurations wrapped around calibrated geometries, generalizing known equations and revealing new geometric structures.

Contribution

It derives generalized Bogomol'nyi equations for intersecting fivebrane configurations, linking BPS states to calibrated geometries in M-theory.

Findings

Derived differential equations generalizing Cauchy-Riemann equations.

Connected BPS configurations to calibrated geometries.

Provided a framework for understanding intersecting brane solutions.

Abstract

The fivebrane worldvolume theory in eleven dimensions is known to contain BPS threebrane solitons which can also be interpreted as a fivebrane whose worldvolume is wrapped around a Riemann surface. By considering configurations of intersecting fivebranes and hence intersecting threebrane solitons, we determine the Bogomol'nyi equations for more general BPS configurations. We obtain differential equations, generalising Cauchy-Riemann equations, which imply that the worldvolume of the fivebrane is wrapped around a calibrated geometry.