Cutoff Scale of Quadratic Gravity from Quantum Focusing Conjecture

TL;DR

This paper determines the cutoff length scale for quadratic gravity in higher dimensions by applying the quantum focusing conjecture, confirming its validity in a specific 5D black hole example.

Contribution

It derives the cutoff scale for quadratic gravity in dimensions five and above using the quantum focusing conjecture, revealing its dependence on the coupling constant sign.

Findings

Cutoff scale depends on spacetime dimension and coupling constant sign.

Quantum focusing conjecture holds when quantum expansion is smeared over scales larger than the cutoff.

Confirmed the conjecture in a 5D Schwarzschild spacetime example.

Abstract

We derive the cutoff length scale of the quadratic gravity in $d \geq 5$ dimensional spacetime by demanding that the quantum focusing conjecture for the smeared quantum expansion holds at the classical level. The cutoff scale has different dependence on the spacetime dimension depending on the sign of the coupling constant of the quadratic gravity. We also investigate a concrete example of the 5-dimensional Schwarzschild spacetime and directly confirm that the quantum focusing conjecture holds when the quantum expansion is smeared over the scale larger than our cutoff scale.