Calibrations, Monopoles and Fuzzy Funnels

TL;DR

This paper introduces new non-Abelian solitonic configurations in D-brane effective theories, revealing how D1-branes can expand into fuzzy funnels ending on intersecting D3-branes, with solutions governed by generalized Nahm's equations.

Contribution

It presents novel solutions to generalized Nahm's equations describing D1-branes expanding into fuzzy funnels on intersecting D3-branes, linking supersymmetry, calibration, and monopole construction.

Findings

Solutions preserve various fractions of supersymmetry.

Configurations relate to self-duality equations in eight dimensions.

Generalized Nahm's equations encode monopole data on calibrated three-surfaces.

Abstract

We present new non-Abelian solitonic configurations in the low energy effective theory describing a collection of N parallel D1--branes. These configurations preserve 1/4, 1/8, 1/16 and 1/32 of the spacetime supersymmetry. They are solutions to a set of generalised Nahm's equations which are related to self-duality equations in eight dimensions. Our solutions represent D1--branes which expand into fuzzy funnel configurations ending on collections of intersecting D3--branes. Supersymmetry dictates that such intersecting D3--branes must lie on a calibrated three-surface of spacetime and we argue that the generalised Nahm's equations encode the data for the construction of magnetic monopoles on the relevant three-surfaces.