Initial value problem in string-inspired nonlocal field theory

Erbin, Harold; Fırat, Atakan Hilmi; Zwiebach, Barton

doi:10.1007/jhep01(2022)167

Title: Initial value problem in string-inspired nonlocal field theory

Journal Article · Thu Jan 27 00:00:00 UTC 2022 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep01(2022)167 · OSTI ID:1909634

^[1];

^[2]; Zwiebach, Barton ^[2]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); National Science Foundation (NSF), Washington, DC (United States). AI Institute for Artificial Intelligence and Fundamental Interactions (IAIFI); Univ. Paris-Saclay, Gif-sur-Yvette (France); Massachusetts Institute of Technology (MIT), Cambridge, MA (United States)
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

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.

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Research Organization:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Organization:: European Union (EU); USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: SC0012567

OSTI ID:: 1909634

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 1 Vol. 2022; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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Title: Initial value problem in string-inspired nonlocal field theory

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