A note on tachyon actions in string theory

TL;DR

This paper investigates how the factorization property of certain string theory fields constrains the form of their spacetime actions, successfully determining the metric-dilaton action and open-string tachyon potential without explicit beta function calculations.

Contribution

It demonstrates that factorization constraints alone can fix the form of key string theory actions and potentials, providing new insights into their structure.

Findings

Fixes the metric-dilaton action form using factorization constraints.

Determines the open-string tachyon potential without beta function computations.

Shows no consistent action exists for the closed-string tachyon with metric and dilaton.

Abstract

A number of spacetime fields in string theory (notably the metric, dilaton, bosonic and type 0 bulk closed-string tachyon, and bosonic open-string tachyon) have the following property: whenever the spacetime field configuration factorizes in an appropriate sense, the matter sector of the world-sheet theory factorizes into a tensor product of two decoupled theories. Since the beta functions for such a product theory necessarily also factorize, this property strongly constrains the form of the spacetime action encoding those beta functions. We show that this constraint alone--without needing actually to compute any of the beta functions--is sufficient to fix the form of the two-derivative action for the metric-dilaton system, as well as the potential for the bosonic open-string tachyon. We also show that no action consistent with this constraint exists for the closed-string tachyon coupled to the metric and dilaton.