Thermal dimension of quantum spacetime

Abstract

Recent results suggest that a crucial crossroad for quantum gravity is the characterization of the effective dimension of spacetime at short distances, where quantum properties of spacetime become significant. This is relevant in particular for various scenarios of "dynamical dimensional reduction" which have been discussed in the literature. We are here concerned with the fact that the related research effort has been based mostly on analyses of the "spectral dimension", which involves an unphysical Euclideanization of spacetime and is highly sensitive to the off-shell properties of a theory. As here shown, different formulations of the same physical theory can have wildly different spectral dimension. We propose that dynamical dimensional reduction should be described in terms of the "thermal dimension" which we here introduce, a notion that only depends on the physical content of the theory. We analyze a few models with dynamical reduction both of the spectral dimension and of our thermal dimension, finding in particular some cases where thermal and spectral dimension agree, but also some cases where the spectral dimension has puzzling properties while the thermal dimension gives a different and meaningful picture.

This V2, while not changing the main results, improves V1 in several ways, including a more in depth analysis of the model in which the thermal dimension only runs at intermediate scales and additional material on the differences between active and passive diffeomorphisms on momentum space

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• On the UV dimensions of Loop Quantum Gravity
• Signal propagation on $\kappa$-Minkowski spacetime and non-local two-point functions
• Cloud of strings in f(R) gravity
• Quantum Gravity on the computer: Impressions of a workshop
• CDT and Cosmology
• Thermal dimensional reduction and black hole evaporation
• Primordial perturbations in a rainbow universe with running Newton constant
• Ultraviolet dimensional reduction of spacetime with zero-point length
• Fractional quantum mechanics meets quantum gravity phenomenology
• The extended phase space thermodynamics of Planck-scale-corrected Reissner-Nordström-anti-de Sitter black hole
• Thermal and spectral dimension of (generalized) Snyder noncommutative spacetimes
• Measurement-Induced Perturbations of Hausdorff Dimension in Quantum Paths
• Response of a canonical ensemble of quantum oscillators to a random metric