Initial value problem in string-inspired nonlocal field theory
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13130_2022_Article_17659.pdf
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Author(s)
Erbin, Harold
Fırat, Atakan H.
Zwiebach, Barton
Date Issued
January 27, 2022
Publisher
Springer Berlin Heidelberg
Citation
Journal of High Energy Physics. 2022 Jan 27;2022(1):167
Version
Final published version
Abstract
Abstract
We consider a nonlocal scalar field theory inspired by the tachyon action in open string field theory. The Lorentz-covariant action is characterized by a parameter ξ2 that quantifies the amount of nonlocality. Restricting to purely time-dependent configurations, we show that a field redefinition perturbative in ξ2 reduces the action to a local two-derivative theory with a ξ2-dependent potential. This picture is supported by evidence that the redefinition maps the wildly oscillating rolling tachyon solutions of the nonlocal theory to conventional rolling in the new scalar potential. For general field configurations we exhibit an obstruction to a local Lorentz-covariant formulation, but we can still achieve a formulation local in time, as well as a light-cone formulation. These constructions provide an initial value formulation and a Hamiltonian. Their causality is consistent with a lack of superluminal behavior in the nonlocal theory.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Department of Physics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1007/JHEP01(2022)167
