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 Padé 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.
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Acknowledgments
We would like to thank H. Erbin for discussions and B. Zwiebach for discussion and helpful comments on the manuscript. We also thank the organizers of the Benasque workshop “Matrix Models and String Field Theory” where some ideas of this paper took shape. The work of T.E. is supported by European Structural and Investment Fund and the Czech Ministry of Education, Youth and Sports (Project CoGraDS - CZ.02.1.01/0.0/0.0/15_ 003/0000437) and the GAČR project 18-07776S and RVO: 67985840. The work of A.H.F. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics of U.S. Department of Energy under grant Contract Number DE-SC0012567.
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Erler, T., Fırat, A.H. Wilsonian effective potentials and closed string field theory. J. High Energ. Phys. 2024, 18 (2024). https://doi.org/10.1007/JHEP02(2024)018
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DOI: https://doi.org/10.1007/JHEP02(2024)018