Geometric tachyon to universal open string tachyon

A system of k Neveu-Schwarz (NS) 5-branes of type II string theory with onetransverse direction compactified on a circle admits various unstable D-branesystems, - some with geometric instability arising out of being placed at apoint of unstable equilibrium in space and some with the usual open stringtachyonic instability but no geometric instability. We discuss the effect of NS5-branes on the descent relations among these branes and their physicalinterpretation in the T-dual ALF spaces. We argue that if the tachyon potentialcontrolling these descent relations obeys certain conditions, then in certainregion in the parameter space labelling the background the two types ofunstable branes become identical via a second order phase transition, with thegeometric tachyon in one system getting mapped to the open string tachyon ofthe other system. This would provide a geometric description of the tachyonicinstability of the usual non-BPS Dp-brane in ten dimensional flat space-time.Comment: LaTeX file, 30 page