Geometric Tachyon to Universal Open String Tachyon

TL;DR

This paper explores how geometric and open string tachyons in unstable D-brane systems are related through phase transitions in backgrounds involving NS 5-branes, providing a geometric perspective on tachyonic instabilities.

Contribution

It demonstrates that under certain conditions, geometric tachyons and open string tachyons become equivalent via a phase transition, linking different unstable brane configurations.

Findings

Geometric and open string tachyons can be mapped onto each other through a second order phase transition.

The phase transition occurs in specific parameter regions of NS 5-brane backgrounds.

The work offers a geometric interpretation of tachyonic instability in non-BPS D-branes.

Abstract

A system of k Neveu-Schwarz (NS) 5-branes of type II string theory with one transverse direction compactified on a circle admits various unstable D-brane systems, - some with geometric instability arising out of being placed at a point of unstable equilibrium in space and some with the usual open string tachyonic instability but no geometric instability. We discuss the effect of NS 5-branes on the descent relations among these branes and their physical interpretation in the T-dual ALF spaces. We argue that if the tachyon potential controlling these descent relations obeys certain conditions, then in certain region in the parameter space labelling the background the two types of unstable branes become identical via a second order phase transition, with the geometric tachyon in one system getting mapped to the open string tachyon of the other system. This would provide a geometric description of the tachyonic instability of the usual non-BPS Dp-brane in ten dimensional flat space-time.