Tachyon condensation on brane sphalerons

TL;DR

This paper models unstable D-branes using sphaleron solutions in a scalar field theory, analyzing tachyon condensation and demonstrating tension cancellation as the circle's size diminishes.

Contribution

It introduces a toy model for unstable D-branes via sphaleron solutions and derives a multiscalar tachyon potential showing tension cancellation.

Findings

Complete tension cancellation at small circle size

Identification of localized tachyon modes in sphaleron spectrum

Development of a multiscalar tachyon potential model

Abstract

We consider a sphaleron solution in field theory that provides a toy model for unstable D-branes of string theory. We investigate the tachyon condensation on a Dp-brane. The localized modes, including a tachyon, arise in the spectrum of a sphaleron solution of a \phi^4 field theory on M^{p+1}\times S^1. We use these modes to find a multiscalar tachyon potential living on the sphaleron world-volume. A complete cancelation between brane tension and the minimum of the tachyon potential is found as the size of the circle becomes small.