Abstract
By using the Born–Infeld action we show that the m circular fundamental strings, n D2-branes and k D0-branes could become a tubular bound state which is prevented from collapsing by the magnetic force in the Melvin background. However, if the ratio m/n is larger then a critical value the tube will become unstable and collapse to zero radius. We make analyses to find the critical value and tube radius therein. The tube configurations we found are different from the well-known tubular bound states of straight fundamental strings, D0- and D2-branes, which are supported by the angular momentum.
Highlights
In an interesting paper [1,2,3], Mateos and Townsend showed that a bunch of straight fundamental strings with D0-branes can be blown-up to a tubular D2-brane
The tube configuration is supported against collapsing by the angular momentum generated by the crossed electric and magnetic Born-Infeld (BI) fields of the straight fundamental strings and D0branes, respectively
We will show that the magnetic force from the Melvin background could prevent the tubular bound configurations of m circular fundamental strings, n D2-branes and k D0-branes from collapsing
Summary
In an interesting paper [1,2,3], Mateos and Townsend showed that a bunch of straight fundamental strings with D0-branes can be blown-up to a tubular D2-brane. The tube configuration is supported against collapsing by the angular momentum generated by the crossed electric and magnetic Born-Infeld (BI) fields of the straight fundamental strings and D0branes, respectively. The background in this case is trivial as there is no external force as that in the Myers effect [4] in which the external RR four-form field could expand D0 branes into the fuzzy sphere to stabilize the system. We will show that the magnetic force from the Melvin background could prevent the tubular bound configurations of m circular fundamental strings, n D2-branes and k D0-branes from collapsing. We show that tubular bound state of m circular fundamental strings, n D2-branes and k D0-branes do not exist in the homogeneous magnetic background [7]
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