Generalized Uncertainty Principle as a Consequence of the Effective Field Theory

Abstract

We will demonstrate that the generalized uncertainty principle exists because of the derivative expansion in the effective field theories. This is because, in the framework of the effective field theories, the minimum measurable length scale has to be integrated away to obtain the low energy effective action. We will analyze the deformation of a massive free scalar field theory by the generalized uncertainty principle, and demonstrate that the minimum measurable length scale corresponds to a second more massive scale in the theory, which has been integrated away. We will also analyze CFT operators dual to this deformed scalar field theory, and observe that scaling of the new CFT operators indicates that they are dual to this more massive scale in the theory. We will use holographic renormalization to explicitly calculate the renormalized boundary action with counterterms for this scalar field theory deformed by the generalized uncertainty principle and show that the generalized uncertainty principle contributes to the matter conformal anomaly.

arXiv comment15 pages, no figures, Accepted for Publication in Physics Letters B

References in corpus (45)

• Gauge Theory Correlators from Non-Critical String Theory
• Large N Field Theories, String Theory and Gravity
• Quantum Gravity at a Lifshitz Point
• Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence
• Lecture Notes on Holographic Renormalization
• Potential Sensitivity of Gamma-Ray Burster Observations to Wave Dispersion in Vacuo
• Quantum gravity and minimum length
• A Generalized Uncertainty Principle in Quantum Gravity
• Noncommutative Field Theory and Lorentz Violation
• Nonstandard optics from quantum spacetime
• Universality of Quantum Gravity Corrections
• Avoiding Dark Energy with 1/R Modifications of Gravity
• A proposal for testing Quantum Gravity in the lab
• Living with Ghosts
• Quantization of Point Particles in 2+1 Dimensional Gravity and Space-Time Discreteness
• Inflation as a Probe of Short Distance Physics
• Derivative Expansion of the Exact Renormalization Group
• Introduction to Effective Field Theory
• The Lee-Wick Standard Model
• Some remarks on high derivative quantum gravity
• The Generalized Uncertainty Principle in (A)dS Space and the Modification of Hawking Temperature from the Minimal Length
• Imprints of Short Distance Physics On Inflationary Cosmology
• Gauge Theories under Incorporation of a Generalized Uncertainty Principle
• Algebraic Holography
• Perturbative Approach to Higher Derivative and Nonlocal Theories
• Generalized uncertainty principles and quantum field theory
• Local Quantum Observables in the Anti-deSitter - Conformal QFT Correspondence
• A Superspace Formulation of The BV Action for Higher Derivative Theories
• Time Crystals from Minimum Time Uncertainty
• Tackling Higher Derivative Ghosts with the Euclidean Path Integral
• Electroweak Theory with a Minimal Length
• Correlation Functions in Holographic Renormalization Group Flows
• Triviality of Higher Derivative Theories
• The minimum length problem of loop quantum cosmology
• Supersymmetry Breaking as a new source for the Generalized Uncertainty Principle
• Space-time deformations as extended conformal transformations
• Generalized Lee-Wick Formulation from Higher Derivative Field Theories
• AdS/CFT Correspondence Beyond its Supergravity Approximation
• On the triviality of higher derivative thoeries
• Quantum Statistical Entropy and Minimal Length of 5D Ricci-flat Black String with Generalized Uncertainty Principle
• Higher-Derivative Boson Field Theories and Constrained Second-Order Theories
• Higher Derivative Fermionic Field Theories
• Pre-Holography
• Holographic Renormalization Group Flows: The View from Ten Dimensions
• Effective Action for the Scalar Field Theory with Higher Vertices

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