Membranes from Five-Branes and Fundamental Strings from Dp Branes

TL;DR

The paper argues that the $M2$-brane appears as a co-dimension three topological soliton on a coincident $M5$-anti-$M5$ pair, and shows that compactification maps brane–antibrane annihilation to fundamental strings via confinement of the overall $U(1)$ on the world-volume. It introduces a topological coupling to $C_3$ through the flux $H=dB$ and demonstrates this mechanism in a toy model with a dual Higgs description for a 2-form gauge field, including flux quantization and finite energy. The results generalize to arbitrary $D_p$-$ar{D}_p$ systems, providing a unified view of how membranes and strings emerge from brane annihilation and resolving a puzzle raised by Witten about the fate of the unbroken $U(1)$. Overall, the work links brane descent, topological solitons, and flux confinement to explain the appearance of lower-dimensional objects in string/M-theory and their dualities.

Abstract

We argue that M2 brane is realized as a topological soliton on a coincident pair of M5 and anti-M5 branes, as the two five-branes annihilate each other. Topology and quantum numbers of this world-volume soliton are discussed in some detail, and its formation is explained qualitatively. It follows from a compactification that a D4-anti-D4 pair annihilate and produce type II fundamental strings. The phenomenon is best described as the confinement of a world-volume U(1) gauge field on D4-anti-D4, where the confined electric flux string is identified as the fundamental string. This generalizes to other D$p$-anti-D$p$ systems, and solves a puzzle recently pointed out by Witten.