Intersecting Branes, Domain Walls and Superpotentials in 3d Gauge Theories

TL;DR

This paper explores how superpotentials in 3d N=2 gauge theories, constructed via branes, can be understood through classical domain wall scattering, linking instanton effects to soliton dynamics.

Contribution

It demonstrates that the superpotential generated by instantons can be interpreted as resulting from classical scattering of domain wall solitons in brane configurations.

Findings

Superpotentials arise from domain wall scattering.

Charged hypermultiplets have non-canonical kinetic terms.

D-branes can be absorbed as BPS lumps at intersections.

Abstract

We revisit the Hanany-Witten brane construction of 3d gauge theories with N=2 supersymmetry. Instantons are known to generate a superpotential on the Coulomb branch of the theory. We show that this superpotential can be viewed as arising from the classical scattering of domain wall solitons. The domain walls live on the worldvolume of the fivebranes and their existence relies on the recent observation that the charged hypermultiplet at the intersection of perpendicular D-branes has non-canonical kinetic terms. We further show how Dp branes may be absorbed at the intersection of perpendicular D(p+4)-branes where they appear as BPS sigma-model lumps.