Nucleation of $P$-Branes and Fundamental Strings

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.