Localized Kaluza-Klein 6-brane

TL;DR

This paper investigates membrane wrapping corrections to the KK6-brane in eleven-dimensional M-theory, revealing how vortex solutions in a gauge theory correspond to instanton effects that explain the brane's localization in extended space.

Contribution

It introduces a gauge theory interpretation of KK6-brane localization via vortex solutions and connects these to M-theory instanton effects, providing new insights into brane dynamics.

Findings

Vortex solutions correspond to localization effects in extended space.

Vortex corrections are interpreted as M-theory instantons.

Dual coordinates are identified through gauge theory vector fields.

Abstract

We study the membrane wrapping mode corrections to the Kaluza-Klein (KK) 6-brane in eleven dimensions. We examine the localized KK6-brane in the extended space in $E_{7(7)}$ exceptional field theory. In order to discuss the physical origin of the localization in the extended space, we consider a probe M2-brane in eleven dimensions. We show that a three-dimensional $\mathcal{N} = 4$ gauge theory is naturally interpreted as a membrane generalization of the two-dimensional $\mathcal{N} = (4,4)$ gauged linear sigma model for the fundamental string. We point out that the vector field in the $\mathcal{N}= 4$ model is identified as a dual coordinate of the KK6-brane geometry. We find that the BPS vortex in the gauge theory gives rise to the violation of the isometry along the dual direction. We then show that the vortex corrections are regarded as an instanton effect in M-theory induced by the probe M2-brane wrapping around the M-circle.