T-duality and the case of the disappearing brane

TL;DR

This paper investigates the apparent paradox of brane creation and disappearance under T-duality in string theory, resolving tensions through supergravity solutions and formulating T-duality relations.

Contribution

It introduces a differential form approach to supergravity T-duality and clarifies the behavior of branes under T-duality involving NS5, D6, D4, and D5-branes.

Findings

Resolved the tension between brane creation and disappearance under T-duality.

Developed a differential form framework for supergravity T-duality relations.

Commented on flux-expulsion properties of D6-branes.

Abstract

When an NS5-brane crosses a D6-brane, a D4-brane is created stretching between them by the Hanany-Witten effect. However, the T-dual situation involves a Kaluza-Klein monopole crossing a D5-brane and should not result in brane creation. Thus, the newly created D4-brane disappears when T-duality is applied. The T-duality is in a direction transverse to the D4-brane so that one would naively have expected the creation of a D5-brane in the T-dual picture. This situation is investigated via the corresponding supergravity solutions and the tension with the naive result is resolved. Along the way, a differential form version of the supergravity T-duality relations is developed and some comments are made concerning the flux-expulsion properties of D6-branes.