Worldsheet Instanton Corrections to the Kaluza-Klein Monopole

TL;DR

This work shows that the unit-charge Kaluza-Klein monopole in string theory receives worldsheet instanton corrections that localize the geometry in winding space, mirroring the localization of the smeared H-monopole under T-duality. By formulating both monopoles as $ ext{N}=(4,4)$ gauged linear sigma models and analyzing point-like instantons, the authors derive a corrected metric and nontrivial torsion, effectively replacing the smeared KK monopole with a winding-space localized configuration in the $g o 0$ limit. The leading instanton contributions yield a corrected harmonic function $H(r, heta)$ and a corresponding torsion $H_{123}=rac{ abla_ heta H}{ abla_ heta}$, consistent with duality to the localized $H$-monopole. These results provide a concrete mechanism for localization in winding space, reveal a throat-like structure controlled by the dual coordinate $ heta$, and motivate further work on the full corrected geometry, higher monopole charges, and possible M-theory extensions.

Abstract

The Kaluza-Klein monopole is a well known object in both gravity and string theory, related by T-duality to a "smeared" NS5-brane which retains the isometry around the duality circle. As the true NS5-brane solution is localized at a point on the circle, duality implies that the Kaluza-Klein monopole should show some corresponding behavior. In this paper, we express the Kaluza-Klein monopole as a gauged linear sigma model in two dimensions and show that worldsheet instantons give corrections to its geometry. These corrections can be understood as a localization in "winding space" which could be probed by strings with winding charge around the circle.