Wilsonian effective potentials and closed string field theory

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.