Midisuperspace quantization: possibilities for fractional and emergent spacetime dimensions

TL;DR

This paper explores how midisuperspace models in quantum gravity can exhibit fractional and emergent spacetime dimensions, revealing a loss of dimensional information and suggesting new avenues for understanding quantum spacetime structure.

Contribution

It demonstrates that midisuperspace models can encode theories with variable, fractional, or emergent dimensions, extending the understanding of quantum gravity corrections beyond classical dimensional constraints.

Findings

Existence of infinitely many second derivative gravity theories in midisuperspace models.

Mapping of certain theories to arbitrary integer dimensions, losing original dimensional information.

Accommodation of fractional and emergent spacetime dimensions in these models.

Abstract

Recently, motivated by certain loop quantum gravity inspired corrections, it was shown that for spherically symmetric midisuperspace models infinitely many second derivative theories of gravity exist (as revealed by the presence of three arbitrary functions in the corresponding Lagrangian/Hamiltonian) and not just those allowed by spherically symmetric general relativity. This freedom can be interpreted as the freedom to accommodate certain quantum gravity corrections in these models even in the absence of higher curvature terms (at a semi-classical level, at least). For a particular choice of the arbitrary functions it is shown that the new theories map to spherically symmetric general relativity in arbitrary number of (integer) dimensions thus explicitly demonstrating that when working with midisuperspace models, one loses the information about the dimensionality of the full spacetime. In addition, it is shown that these new theories can accommodate scenarios of fractional spacetime dimensions as well as those of emergent spacetime dimensions -- a possibility suggested by various approaches to quantum gravity.