Nucleation of $P$-Branes and Fundamental Strings

TL;DR

This paper constructs and analyzes solutions describing the nucleation and stability of fundamental strings and p-branes in string theory backgrounds, including instantons and unstable equilibria, revealing new insights into brane dynamics and instabilities.

Contribution

It introduces explicit solutions for nucleation processes and stability analysis of strings and p-branes in various string theory backgrounds, extending previous understanding of brane instabilities.

Findings

Constructed a solution for an expanding fundamental string loop in a background H-field.

Calculated the nucleation rate of a fundamental string loop in this background.

Demonstrated instability of magnetic fluxbranes to nucleation of charged p-branes.

Abstract

We construct a solution to the low-energy string equations of motion in five dimensions that describes a circular loop of fundamental string exponentially expanding in a background electric $H$-field. Euclideanising this gives an instanton for the creation of a loop of fundamental string in a background $H$-field, and we calculate the rate of nucleation. Solutions describing magnetically charged strings and $p$-branes, where the gauge field comes from Kaluza-Klein reduction on a circle, are also constructed. It is known that a magnetic flux tube in four (reduced) spacetime dimensions is unstable to the pair creation of Kaluza-Klein monopoles. We show that in $(4+p)$ dimensions, magnetic $(p+1)$ ``fluxbranes" are unstable to the nucleation of a magnetically charged spherical $p$-brane. In ten dimensions the instanton describes the nucleation of a Ramond-Ramond magnetically charged six-brane in type IIA string theory. We also find static solutions describing spherical charged $p$-branes or fundamental strings held in unstable equilibrium in appropriate background fields. Instabilities of intersecting magnetic fluxbranes are also discussed.