Wilsonian effective potentials and closed string field theory

TL;DR

This paper explores the use of Wilsonian effective field theory to analyze the nonperturbative vacuum structure of closed string field theory, finding universal features and proposing computational methods for better approximations.

Contribution

It demonstrates that Wilsonian effective potentials can exactly capture nonperturbative vacua in closed string field theory and suggests practical truncation and resummation techniques for future calculations.

Findings

Effective potentials contain the same nonperturbative vacua as the original Lagrangian.

Universal features are observed in the effective potential across cases.

Padé resummation helps approximate the global structure of the potential.

Abstract

We investigate Wilsonian effective field theory as a model for the construction of the tachyon potential and nonperturbative vacua in closed string field theory. In a number of cases we are able to find the effective potential exactly, and observe what appear to be universal features. We find that the effective field theory contains the same nonperturbative vacuum structure as the bare Lagrangian, though this information is encoded less efficiently as the distance scale of the effective field theory is increased. The implication is that closed string field theory plausibly contains information about the nonperturbative vacuum structure of string theory, in spite of its similarities to effective field theory. We also truncate the effective potential at a fixed power of the field and investigate how the global structure of the effective potential may be approximated via Pad\'e resummation. Qualitative comparisons suggest that computation of the eighth to sixteenth order closed string vertex should be enough to obtain reliable results for the closed string field theory action evaluated on the tachyon field.