Gauge Invariant Action for the Open Bosonic String: Tachyon Action

TL;DR

This paper develops a gauge invariant action for the open bosonic string focusing on the tachyon mode, demonstrating its consistency with equations of motion, beta functions, and Sen's conjecture through perturbative calculations and renormalization techniques.

Contribution

It provides a detailed perturbative analysis of the tachyon action within a gauge invariant framework, including renormalization and the derivation of the tachyon potential.

Findings

The cubic tachyon action reproduces correct equations of motion.

The theory can be renormalized to eliminate cutoff dependence.

The tachyon potential matches Sen's conjecture on brane tension.

Abstract

A gauge invariant action for the open bosonic string has been proposed in an earlier paper. We work out the consequences of this proposal for the lowest mode, viz. the tachyon. The action can be calculated for generic momenta, perturbatively, order by order in the tachyon field. For on shell tachyons we explicitly calculate the cubic action and show that it reproduces the correct equations of motion and coincides wih the $\beta$ function to the required order. The calculation is done in terms of bare fields with a finite cutoff, which is the original prescription. We also show that it is possible in some momentum regions to renormalize the theory and eliminate the cutoff dependence so that the continuum limit can be taken. After renormalization, the parameter $R\over a$ is replaced by $R\over L$ where $R$ is an IR cutoff, $a$ is the UV cutoff and $L$ is some renormalization scale. There is also some arbitrariness in the overall normalization due to the choice of regularization scheme - this does not affect on-shell quantities. We also rederive within this scheme, the action in the region of zero momentum, which gives the exact (tree level) tachyon potential. The tachyon potential is consistent with Sen's conjecture that the height of the potential is the same as the tension of the brane.