Tachyons on Dp-branes from Abelian Higgs sphalerons

TL;DR

This paper models tachyon condensation on Dp-branes using an Abelian Higgs framework, demonstrating algebraic normal modes and confirming Sen's conjecture through explicit potential calculations.

Contribution

It introduces a field theoretical toy model with quasi-exactly solvable sphaleron solutions to study tachyon condensation on Dp-branes, providing explicit normal modes and potential analysis.

Findings

Normal mode equations are quasi-exactly solvable for specific mass ratios.

Exact cancellation between tachyon potential energy and brane tension is demonstrated.

Supports Sen's conjecture with explicit calculations in a simplified model.

Abstract

We consider the Abelian Higgs model in a (p+2)-dimensional space time with topology M^{p+1} x S^1 as a field theoretical toy model for tachyon condensation on Dp-branes. The theory has periodic sphaleron solutions with the normal mode equations resembling Lame-type equations. These equations are quasi-exactly solvable (QES) for specific choices of the Higgs- to gauge boson mass ratio and hence a finite number of algebraic normal modes can be computed explicitely. We calculate the tachyon potential for two different values of the Higgs- to gauge boson mass ratio and show that in comparison to previously studied pure scalar field models an exact cancellation between the negative energy contribution at the minimum of the tachyon potential and the brane tension is possible for the simplest truncation in the expansion about the field around the sphaleron. This gives further evidence for the correctness of Sen's conjecture.