Remarks on noncommutative solitons

Abstract

In the first part of this work we consider an unstable non-BPS $Dp-\bar{Dp}-$brane pair in Type II superstring theory. Turning on a background NS-NS $B-$field (constant and nonzero along two spatial directions), we show that the tachyon responsible for the unstability has a complex GMS solitonic solution, which is interpreted as the low energy remnant of the resulting $D(p-2)-$brane. In the second part, we apply these results to construct the noncommutative soliton analogous of Witten's superconducting string. This is done by considering the complex GMS soliton arising from the $D3-\bar{D3}-$brane annihilation in Type IIB superstring theory. In the presence of left-handed fermions, we apply the Weyl-Wigner-Moyal correspondence and the bosonization technique to show that this object behaves like a superconducting wire.