Initial value problem in string-inspired nonlocal field theory

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 ${\xi }^2$ that quantifies the amount of nonlocality. Restricting to purely time-dependent configurations, we show that a field redefinition perturbative in ${\xi }^2$ reduces the action to a local two-derivative theory with a ${\xi }^2$-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.

arXiv comment49 pages, 14 figures

References in corpus (60)

• k-Inflation
• Rolling Tachyon
• Perturbations in k-inflation
• Causality, Analyticity and an IR Obstruction to UV Completion
• Tachyon Matter
• Black Hole Entropy in Canonical Quantum Gravity and Superstring Theory
• k-Essence, superluminal propagation, causality and emergent geometry
• Spacelike Branes
• Tachyon condensation in string field theory
• Dynamics with Infinitely Many Time Derivatives and Rolling Tachyons
• Direct measurement of superluminal group velocity and of signal velocity in an optical fiber
• Black Hole Complementarity vs. Locality
• Dynamics with Infinitely Many Derivatives: The Initial Value Problem
• Nonlocal and quasi-local field theories
• Analytic Solutions for Marginal Deformations in Open String Field Theory
• Comments on Marginal Deformations in Open String Field Theory
• Cutkosky Rules for Superstring Field Theory
• Locality in quantum gravity and string theory
• Closed Superstring Field Theory and its Applications
• Duality Invariant Cosmology to all Orders in ${\alpha }^{\prime }$
• Hamiltonian Formalism for Space-time Non-commutative Theories
• Nonviolent nonlocality
• Gravitational effects in ultrahigh-energy string scattering
• Superluminality and UV Completion
• The closed string tadpole in open string field theory
• Neural Networks and Quantum Field Theory
• Tachyon condensation in open-closed p-adic string theory
• Field redefinitions in effective theories at higher orders
• Causality in Curved Spacetimes: The Speed of Light & Gravity
• Causality and Micro-Causality in Curved Spacetime
• Solutions from boundary condition changing operators in open string field theory
• A Solvable Toy Model for Tachyon Condensation in String Field Theory
• Nonlocality vs. complementarity: a conservative approach to the information problem
• Strings Near a Rindler Or Black Hole Horizon
• The boundary state from open string fields
• Stress Tensors in p-adic String Theory and Truncated OSFT
• Boundary State from Ellwood Invariants
• Information Spreading in Interacting String Field Theory
• Physical Degrees of Freedom of Non-local Theories
• Time Dependent Solution in Cubic String Field Theory
• Causality and Unitarity via the Tree-Loop Duality Relation
• Nonperturbative renormalization for the neural network-QFT correspondence
• Hyperbolic three-string vertex
• Open-closed Hyperbolic String Vertices
• Rolling to the tachyon vacuum in string field theory
• String-theoretic breakdown of effective field theory near black hole horizons
• Mapping between Witten and Lightcone String Field Theories
• Analyticity and Crossing Symmetry of Superstring Loop Amplitudes
• Comments on gauge invariant overlaps for marginal solutions in open string field theory
• Locality, Causality, and an Initial Value Formulation for Open String Field Theory
• Black hole complementarity: the inside view
• Quantum Corrections in p-adic String Theory
• Rolling Near the Tachyon Vacuum
• String Theory and Black Hole Complementarity
• Long-Range Nonlocality in Six-Point String Scattering: simulation of black hole infallers
• Recovering Infalling Information via String Spreading
• String Field Theory in Rindler Space-Time and String Thermalization
• Entanglement Entropy in Closed String Theory
• Analyticity of Off-shell Green's Functions in Superstring Field Theory
• Analyticity Domain for Off-shell Five-point Superstring Loop Amplitudes

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• Boundary terms in string field theory
• String vertices for the large $N$ limit
• 2D Black Holes, Bianchi I Cosmologies, and ${\alpha }^{\prime }$
• A boundary term for open string field theory
• Topological defects in nonlocal field theories
• Symplectic structure in open string field theory I: Rolling tachyons
• Massive to Massless by Applying a Nonlocal Field Redefinition
• Fractional Particle and Sigma Model
• Evolutionary algorithms for multi-center solutions
• Classifying deviation from standard quantum behavior using Kullback Leibler divergence
• UV Effects and Short-Lived Hawking Radiation: Alternative Resolution of Information Paradox
• Towards Hamiltonian Formalism for String Field Theory and Nonlocality