Nonlocality in string theory

Abstract

We discuss an aspect of string theory which has been tackled from many different perspectives, but incompletely: the role of nonlocality in the theory and its relation to the geometric shape of the string. In particular, we will describe in quantitative terms how one can zoom out from an extended object such as the string in such a way that, at sufficiently large scales, it appears structureless. Since there are no free parameters in free-string theory, the notion of large scales will be unambiguously determined. In other words, we will be able to answer the question: How and at which scale can the string be seen as a particle? In doing so, we will employ the concept of spectral dimension in a new way with respect to its usual applications in quantum gravity. The operational notions of worldsheet and target spacetime dimension in string theory are also clarified and found to be in mutual agreement.

13 pages, 2 figures. v2: derivation of the nonlocal model considerably expanded and clarified, derivation of the spacetime spectral dimension expanded in full with one figure added, typos corrected, main results and conclusions unchanged

References in corpus (4)

• Localization of nonlocal theories
• Dynamics with Infinitely Many Derivatives: The Initial Value Problem
• Trace Anomaly in Quantum Spacetime Manifold
• Thermodynamics of photons on fractals

Cited by in corpus (43)

• Nonlocal quantum gravity and M-theory
• Constraining Generalized Non-local Cosmology from Noether Symmetries
• Super-accelerating bouncing cosmology in asymptotically-free non-local gravity
• Dimensional flow in discrete quantum geometries
• Gravitational-wave luminosity distance in quantum gravity
• Nonlocal Teleparallel Cosmology
• Multiscale spacetimes from first principles
• Constraining Non-local Gravity by S2 star orbits
• Considerations on gravitational waves in higher-order local and non-local gravity
• The gravitational energy-momentum pseudo-tensor of Higher-Order Theories of Gravity
• ABC of multi-fractal spacetimes and fractional sea turtles
• Imprint of quantum gravity in the dimension and fabric of spacetime
• Quantum spectral dimension in quantum field theory
• Foundations of ghost stability
• Mass Gap in Infinite Derivative Non-local Higgs: Dyson-Schwinger Approach
• Standard Model in multiscale theories and observational constraints
• Higgs Mechanism in Nonlocal Field Theories
• Quantum gravity without vacuum dispersion
• Unruh effect of nonlocal field theories with a minimal length
• Strongly Coupled String-inspired Infinite Derivative Non-local Yang-Mills: Diluted Mass Gap
• Muon $g-2$ anomaly and non-locality
• Hypothesis on the Nature of Time
• Quintessence Dark Energy from strongly-coupled Higgs mass gap: Local and Non-local higher-derivative non-perturbative scenarios
• One-loop effective potential in the non-local supersymmetric gauge theory
• Logarithmic corrections to Newtonian gravity and Large Scale Structure
• Asymptotic nonlocality
• Dimensional flow in the kappa-deformed space-time
• Worldline theories with towers of internal states
• Non-perturbative Lee-Wick gauge theory: Towards Confinement and RGE with strong couplings
• Finite entanglement entropy and spectral dimension in quantum gravity
• The 1.5 post-Newtonian radiative quadrupole moment in the context of a nonlocal field theory of gravity
• Fate of the false vacuum in string-inspired nonlocal field theory
• Rainbow Spacetime from a Nonlocal Gravitational Uncertainty Principle
• Nonlocal dynamics and infinite non-relativistic conformal symmetries
• Fractional Particle and Sigma Model
• On the Meaning of Localization in Non-Local Quantum Field Theory and On the Limits of a Space-Time Description and the Physical Meaning of Phase Space in a Nonlocal Continuum
• Nonlocal scalar field in an external potential: WKB approximation
• Joining Spacetimes on Fractal Hypersurfaces
• Cosmology of fractional gravity
• Towards Hamiltonian Formalism for String Field Theory and Nonlocality
• Nonlocality in Quantum Gravity and the Breakdown of Effective Field Theory
• Renormalisable Non-local Quark-Gluon Interaction: Mass Gap, Chiral Symmetry Breaking & Scale Invariance
• Inflationary $\alpha$-Attractor From Type IIB/F Theory