Generalized Uncertainty Principle as a Consequence of the Effective Field Theory

TL;DR

This paper shows that the generalized uncertainty principle naturally arises from the derivative expansion in effective field theories, linking it to integrated-out high-energy scales and their holographic duals, affecting conformal anomalies.

Contribution

It demonstrates that the GUP results from derivative expansion in effective field theories and explores its implications via holographic duality and conformal anomalies.

Findings

GUP corresponds to a second, more massive scale in the theory.

Deformation affects the scaling of dual CFT operators.

GUP contributes to the matter conformal anomaly.

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.