Evidence for asymptotic safety from lattice quantum gravity

Area of Science:

• Theoretical Physics
• Quantum Gravity
• Cosmology

Background:

• Understanding quantum gravity is crucial for unifying general relativity and quantum mechanics.
• The spectral dimension offers insights into the effective dimensionality of spacetime at different scales.
• Previous studies using Causal Dynamical Triangulations (CDT) showed similar spectral dimension behavior.

Purpose of the Study:

• To calculate the spectral dimension for nonperturbative quantum gravity using Euclidean Dynamical Triangulations (EDT).
• To investigate the implications of the calculated spectral dimension for reconciling major theoretical frameworks.
• To address the apparent conflict between asymptotic safety and the holographic principle.

Main Methods:

• Nonperturbative quantum gravity calculations.
• Euclidean Dynamical Triangulations (EDT) approach.
• Spectral dimension analysis across various distance scales.

Main Results:

• The spectral dimension was found to run from approximately 3/2 at short distances to 4 at large distances.
• This running behavior mirrors findings from Causal Dynamical Triangulations (CDT).
• The short-distance value of 3/2 was identified as a potential resolution to theoretical tensions.

Conclusions:

• The EDT approach yields a spectral dimension consistent with CDT.
• The short-distance spectral dimension of 3/2 provides a bridge between asymptotic safety and the holographic principle.
• This finding advances our understanding of quantum gravity's dimensional flow.